Class 6 Maths - Knowing Our Numbers

Subtract:
$$3xy + 5yz- 7zx$$ from $$5xy -2yz- 2zx + 10xyz$$

Subtract $$3xy + 5yz-7zx$$ from$$5xy - 2yz - 2zx + 10xyz$$
$$5xy - 2yz - 2zx + 10xyz-(3xy + 5yz-7zx)$$
$$=5xy - 2yz - 2zx + 10xyz-3xy - 5yz+7zx$$
$$=2xy-7yz+5zx+10xyz$$

Four numbers $$3, 1, 2$$ and $$5$$ are given. Form a four digit number from these given numbers such that the digits in the final number are in increasing order.

Numbers given are $$3,1,2,5$$

Arranging the digits in ascending order, we get $$1,2,3,5$$

$$\therefore$$ Four digit number formed from these numbers such that digits of final number are in increasing order is $$= 1235$$

Bhanu bought 3 kg 500 gm of jalebi, 2 kg 250 gm of Mysore Pak and 1 kg 750 gm badhushaw, and 750 gm of Jamun. What is the total weight of the sweets that Bhanu bought?

We have:

Jalebi $$=3kg \ 500gm$$

Mysore Pak $$=2kg \ 250gm$$

Badhushaw $$=1kg \ 750gm$$

Jamun $$=\ 750gm$$

Now,

Add all the amount in kg first we get,

$$\left( 3kg+2kg+1kg \right) =5kg$$

Now add the weight given in gm we get,

$$\left( 500g+250g+750g+750g \right) =2250g=2kg250gm$$

So total weight =

$$\left( 5kg+2kg\ 250\ gm \right) =7kg\ 250\ gm$$

Compute the following:
$$100+(-80)$$

To compute the following

$$ 100 + (-80) $$

As we know that $$ (+) \times (-) = - $$

Therefore, we have

$$ = 100 - 80 $$

$$ = 20 $$

Compute the following:
$$14+(-10)$$

To compute the following

$$ 14 + (-10) $$

As we know that $$ (+) \times (-) = - $$

Therefore, we have

$$ = 14 -10 $$

$$ = 4 $$

Compute the following:
$$225+(-145)$$

To compute the following:

$$ 225 + (-145) $$

As we know that $$ (+) \times (-) = - $$

Therefore, we have

$$ = 225 -145 $$

$$ = 80 $$

Compute the following:
$$10+(-2)$$

To compute the following

$$ 10 + (-2) $$

As we know that $$ (+) \times (-) = (- )$$

Therefore on Adding

$$ = 10 - 2 $$

$$ = 8 $$

Compute the following:
$$13+(-15)$$

To compute the following

$$ 13 + (-15) $$

On adding, we have

$$ = 13 -15 $$

$$ = -2 $$

How many dozen bananas are there in 216 bananas?

Number of bananas in a dozen $$=12$$

Therefore, number of dozens there in $$216$$ bananas $$=216\div12=18$$

Compute the following:
$$7+4$$

To compute the following:

$$ 7 + 4 $$

On adding these $$2$$, we get

$$ 7 + 4 $$

$$ = 11 $$

In its search for water a frog fell down into a $$30m$$ deep well. Its progress out of the well was very erratic. Each day it managed to climb up $$3\ m$$, but the following night , it slipped back $$2\ m$$. How many days did it take to get out of the well?

Depth of well $$= 30 m$$

If each day frog managed to climb up $$3 m,$$ but the following night, it slipped back $$2 m$$ then,

Frog climb $$1 m$$ in one day and it climb $$27 m$$ in $$27$$ days

On $$28$$ th day it climb $$3 m$$ and it get out of the well

So, total days it take to get out of the well $$= 28 days$$ (Ans)

Solve the following:
$$80-(-50)$$

To Solve the following

$$ 80 - (-50) $$

As we know that $$(-)\times(-) = +$$

$$ 80 + 50 $$

$$ = 130 $$

Hence , Finally we get

$$ = 130 $$

Fill in the following blanks:
_____ $$ \div 1=-49$$

_____ $$\div 1 = -49 $$

Let the unknown be "$$x$$"

Then, $$ x\div 1 = -49 $$

Therefore, we have

$$ x= \dfrac{-49}{1} $$

$$ x= -49 $$

Hence, $$ (-49) \div 1 = -49 $$

Solve the following:
$$32-(-18)$$

To Solve the following

$$ 32 - (-18) $$

As we know that $$ (-) \times (-) = + $$

Therefore , on Solving this

$$ 32 + 18 $$

$$ = 50 $$

Write the number names according to :
Number Indian System International system
236749
48670002

$$236749$$

Indian system : $$2,36,749$$ - Two lakh thirty six thousand seven hundred forty nine

International system : $$236,749$$ - Two hundred thirty six thousand seven hundred forty nine

$$48670002$$

Indian system : $$4,86,70,002$$ - Four Crore Eighty Six lakh Seventy thousand two

International system : $$48,670,002$$ - Forty Eight million Six hundred seventy thousand two

Solve the following:
$$150-75$$

To Solve the following

$$ 150 - 75 $$

On Subtracting this we get

$$ 150 - 75 $$

$$ = 75 $$

Solve the following:
$$25-33$$

To Solve the following

$$ 25 - 33 $$

This can be written as

$$ -33 + 25 $$

$$ = -8 $$

Hence , Finally we get

$$ = -8 $$

Add $$48 + 49 + 31 + 30 = \_\_\_\_\_$$

$$48+49+31+30$$

$$=158$$

How many five thousands are there in one lakh?

Divide $$100000$$ by $$5000$$ to get the number of five thousand in one lakh.

$$\therefore$$ 20 five thousands are there in one lakh.

The number $$6778243$$ should properly be written as_______________

The number is properly written as $$67,78,243$$

Solve $$5+(-4)+1$$

given $$5 +(-4)+1$$

$$\Rightarrow 5-4+1=2$$

therefore the value is 2

Add $$48$$+$$49$$+$$31$$+$$30$$

$$48 + 49 +31 +30=158$$

Subtract the sum of $$-1032$$ and $$878$$ from $$-34$$.

The sum of $$-1032$$ and $$879=(-1032)+878 $$

$$=-154$$

Now we subtract $$-154$$ from $$-34$$

I.e., $$(-34)-(-154)=-34+154=120$$

Ans: $$120$$

Subtract $$635$$ from $$-547$$

$$-547-635 = -1182$$

Answer is $$-1182$$

Arrange in ascending order.
$$\dfrac{14}{25}, \dfrac{18}{27}, \dfrac{16}{21}, \dfrac{12}{24}, \dfrac{17}{29}$$

Solution:-

Numbers are said to be in ascending order when they are arranged from the smallest to the largest number.

$$\therefore$$ Ascending orderof given numbers is-

$$\cfrac{12}{24} < \cfrac{14}{25} < \cfrac{17}{29} < \cfrac{18}{27} < \cfrac{16}{21}$$

Mohit travelled in a bus towards $$east$$ $$of$$ $$Delhi$$ by $$49km$$ then towards $$west$$ $$of$$ $$Delhi$$ by $$80km$$. How far was he from Delhi?

Mohit goes east $$49\,Km\,\& $$

then west $$80Km$$

from Delhi he is$$\left( {80 - 49} \right)Km$$$$=31Km$$

Fill in the blanks with $$<$$ or $$>$$ sign.
$$34512$$ ________ $$5451$$.

Let $$a = 34512$$ and $$b = 5451$$

Now, $$a-b=34512- 5451$$

$$ = 29061 > 0$$

So, $$a-b > 0$$

$$\Rightarrow a > b$$

So, $$34512 > 5451$$

Which is the bigger and which the smaller number?
$$423\ \Box\ 723$$

$$721=7\times 10^2+2\times 10+1$$ is smaller.

$$723=7\times 10^2+2\times 10+3$$ is bigger.

$$721 < 723$$

Simplify:
$$28-3\times 5+4$$
$$42-18\div 2\times 3$$

1.$$28-3\times 5+4=28-15+4$$

$$=17$$

2.$$42-18\div 2\times 3=42-9\times 3$$

$$=42-27$$

$$=15$$

Which is the bigger and which the smaller number?
$$721\ \Box\ 589$$

$$721=7\times 10^2+2\times 10+1$$ is bigger.

$$589=5\times 10^2+8\times 10+9$$ is smaller.

$$721 > 589$$

Simplify
$$\sqrt{50}-\sqrt{98}$$

$$\sqrt{50}-\sqrt{98}$$

$$\Rightarrow$$ $$\sqrt{25\times 2}-\sqrt{49\times 2}$$

$$\Rightarrow$$ $$\sqrt{25}.\sqrt{2}-\sqrt{49}.\sqrt{2}$$

$$\Rightarrow$$ $$5\sqrt{2}-7\sqrt{2}$$

$$\Rightarrow$$ $$-2\sqrt{2}$$

$$\Rightarrow$$ $$-2\times (1.414)$$

$$\Rightarrow$$ $$-2.828$$

Rama left her home on the morning of $$11.11.2015$$ and came back home at the night of $$12.12.2016$$. For how many days was she remain away from home.

No. of days between $$11.11.2015$$ and $$10.11.2016=366$$ [leap year]

No. of days between $$11.11.2016$$ and $$30.11.2016=20$$

No. of days between $$1.12.2016$$ and $$12.12.2016=12$$

Total no. of days$$=366+20+12$$

$$=398$$ days

Simplify:
$$\cfrac{27}{9}+(27-1)\cfrac{9}{27}$$

$$\dfrac{27}{9}+\left(27-1\right)\dfrac{9}{27}$$

$$ =\dfrac{27}{9}+27\times \dfrac{9}{27}-\dfrac{9}{27}$$

$$ =\dfrac{27}{9}+9-\dfrac{1}{3}$$

$$ =3+9-\dfrac{1}{3} = \left(3-\dfrac{1}{3}\right)+9$$

$$ =\dfrac{8}{3}+9=\dfrac{8+27}{3} = \dfrac{35}{3}$$

$$LXXXI$$= _______ (Write the value in Hindu - Arabic number,)

$$LXXXI=81$$

$$L=50, X=10 \,and\, I=1$$

$$LXXXI= 50+10+10+10+1=81$$

Write the Roman numerals for the following:
$$94$$

$$94$$ can be written as $$(90+4)\Rightarrow (100-10+4)$$

Therefore, $$\Rightarrow 94=XCIV$$

Find the value of x $$\cfrac { 17.28\div x }{ 3.6\times 0.2 } =2$$

$$\cfrac { 17.28\div ? }{ 3.6\times 0.2 } =2$$

$$\cfrac { \left[ \left( 1728 \right) \times { 10 }^{ -2 } \right] }{ ? } =2\times 36\times 2\times { 10 }^{ -2 }$$

$$\cfrac { { 12 }^{ 3 } }{ ? } ={ 12 }^{ 2 }$$

$$\therefore ?=12$$

Write the Roman numerals for the following:
$$550$$

$$550$$ can be written as $$(500+50)$$

Therfore, $$\Rightarrow 550=DL$$

What should be added to $$(2\cfrac{1}{3}+2\cfrac{2}{5})$$ to get the sum $$10$$?

Let the x be the number we have to add to make the sum equal to 10

$${ x }+{ 2 }\dfrac { 1 }{ 3 } +{ 2 }\dfrac { 2 }{ 5 } ={ 10 }\\ \Rightarrow { x }+\frac { 7 }{ 3 } +\frac { 12 }{ 5 } =10\\ \Rightarrow { x }+\dfrac { 53+36 }{ 15 } =10\\ \Rightarrow { x }={ 10 }-\dfrac { 89 }{ 15 } \\ \quad \quad \quad =\dfrac { 150-89 }{ 15 } =\dfrac { 61 }{ 15 } \\ \Rightarrow { x }={ 4 }\dfrac { 1 }{ 15 } \\ $$

Solve $$\dfrac{2}{7} - \left( {\dfrac{{ - 5}}{6}} \right)$$

We have,

$$\dfrac{2}{7}-\left( -\dfrac{5}{6} \right)$$

$$ =\dfrac{2}{7}+\dfrac{5}{6} $$

$$ =\dfrac{12+35}{42} $$

$$ =\dfrac{47}{42} $$

Hence, this is the answer.

Write the Roman numerals for the following:
$$260$$

$$260$$ can be written as $$(100+100+50+10)$$

Therefore, $$\Rightarrow 260=CCLX$$

Write the Roman numerals for the following:
$$900$$

$$900$$ can be written as $$(1000-100)$$

Therefore, $$\Rightarrow 900=CM$$

Write the Roman numerals for the following:
$$120$$

$$120$$ can be written as $$(100+10+10)$$

Therefore, $$\Rightarrow 120=CXX$$

Madhu buys $$5\ kg$$ of potatoes at the market. If the cost of $$2\ kg$$ is $$Rs. 36$$, how will Madhu pay?

Given that the $$2\,kg$$ Potatoes $$=Rs.36$$

So, the $$1\,kg$$ Potatoes $$=\dfrac{36}{2}=Rs.18$$

Since, Madhu buys $$5\,kg$$ Potatoes $$=18\times 5=Rs.90$$.

Hence, Madhu will pay $$Rs. 90$$.

Hence, this is the answer.

Subtract the sum of $$1\cfrac{7}{10}$$ and $$2\cfrac{1}{5}$$ from $$5$$

At first add both the number

$${ 1 }\dfrac { 7 }{ 10 } +{ 2 }\dfrac { 1 }{ 5 } \\ =\dfrac { 17 }{ 10 } +\dfrac { 11 }{ 5 } \\ =\dfrac { 17+22 }{ 10 } \\ =\dfrac { 39 }{ 10 } $$

Substract the summ of both nuber from 5 as follow:-

$$\\ { 5 }-\dfrac { 39 }{ 10 } \\ =\dfrac { 50-39 }{ 10 } \\ =\dfrac { 11 }{ 10 } \\ ={ 1 }\dfrac { 1 }{ 10 } $$

Add $$6\frac{2}{3} + 4\frac{3}{5}$$ and subtract $$4\frac{2}{7} - 3\frac{3}{7}$$

We have,

$$=6\dfrac{2}{3}+4\dfrac{3}{5}$$

$$ =\dfrac{20}{3}+\dfrac{23}{5} $$

$$ =\dfrac{100+69}{15} $$

$$ =\dfrac{169}{15} $$

Since,

$$ =4\dfrac{2}{7}-3\dfrac{3}{7} $$

$$ =\dfrac{30}{7}-\dfrac{24}{7} $$

$$ =\dfrac{30-24}{7} $$

$$ =\dfrac{6}{7} $$

Hence, this is the answer.

Solve : $$2a - [4b - \{4a - (3b - \overline{2a + 2b})\}]$$

$$2a−[4b−{4a−(3b−\bar{2a+2b})}]$$

$$2a−[4b−{4a−(3b−2(a+b))}]$$

$$2a−[4b−{4a−(3b−2a-2b)}]$$

$$2a−[4b−{4a−(b−2a)}]$$

$$2a−[4b−{4a−b+2a)}]$$

$$2a−[4b−{6a−b)}]$$

$$2a−[4b−6a+b]$$

$$2a−[5b−6a]$$

$$2a−5b+6a$$

$$8a−5b$$

Subtract the sum of $$-48$$ and $$-58$$ from $$102$$.

$$sum of -48 and -58 is=-106$$

$$=102-(-106)$$

$$=102+106$$

$$=208$$

If $$a = 2$$ and $$b = 3$$, find the value of $$a + b$$.

a+b=2+3

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$3x - 2y + z$$.

3*1-2*2+5

3-4+5

8-4

If $$a = 2$$ and $$b = 3$$, find the value of $$5a^{2} - 2ab$$.

5*(2*2)-2*2*3

20-12

If $$a = 2$$ and $$b = 3$$, find the value of $$a^{3} - b^{3}$$.

(2*2*2)-(3*3*3)

8-27

-18

If $$a = 2$$ and $$b = 3$$, find the value of $$2a - 3b$$.

Given that,

$$a=2 \text{ and }b=3$$

To evaluate:

$$2a-3b\quad ......(i)$$

Substituting the values of $$a$$ and $$b$$ in $$(i)$$, we get:

$$2(2)-3(3)$$

$$\Rightarrow 4-9=-5$$

$$\therefore \ 2a-3b=-5$$

Hence, if $$a=2$$ and $$b=3$$, the value of $$2a-3b$$ is $$-5$$.

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$2x^{2} y - 5yz + xy^{2}$$.

2*1*1*2-5*2*5+1*2*2

4-50+4

8-50

-42

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$xy + yz - zx$$.

1*2+2*5-5*1

2+10-5

12-5

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$x^{3} - y^{3} - z^{3}$$.

1*1*1-2*2*2-5*5*5

1-8-125

-132

Verify the following: $$\left (-13\right)x\left[\left(-6\right)+\left (-19\right)\right]=\left (-13\right)x\left (-6\right)+\left (-13\right)x\left (-19\right)$$.

Solving using BODMAS,

LHS,

$$(-13)x[-25]$$

$$\implies 325x$$

RHS,

$$78x+247x$$

$$\implies 325x$$ = LHS

Hence, proved

Evaluate:
$$\dfrac {7}{13}+\dfrac {-4}{39}$$

Given

$$\dfrac{7}{13}+\dfrac{-4}{39}$$

$$=\dfrac{7}{13}-\dfrac{4}{39}$$

$$=\dfrac{21-4}{39}$$

$$=\dfrac{17}{39}$$

Express in Roman numerals :
i) $$105$$
ii) $$511$$

Required numerals,

1. $$105= CV$$

2. $$511=DXI$$

What should be added to $$729.28$$ to get $$1000$$?

number to be added is=1000-729.28=27.072

Subtract $$0.5-0.49$$

$$+0.50$$

$$\underline{-0.49}$$

$$+0.01$$

Therefore, $$0.5-0.49=0.01$$

$$1$$ million $$=$$ ____ hundred thousands.

$$1 \space million=10,00,000=10\times 1,00,000=10\space hundred\space thousands$$

The sum of two numbers is $$30.64$$. If one of the numbers is $$21.28$$, find the other.

Sum of two numbers $$=30.64$$

First number $$=21.28$$

Other number $$= \text{Sum - First number} = 30.64-21.28$$

$$=9.36$$

Substact the sum of $$\dfrac{2}{7}$$ and $$-\dfrac{4}{21}$$ from $$\dfrac{1}{21}$$

According to the question

$$\dfrac{1}{21}-\left(\dfrac{2}{7}+\left(-\dfrac{4}{21}\right)\right)$$

$$=\dfrac{1}{21}-\left(\dfrac{2}{7}-\dfrac{4}{21}\right)$$

$$=\dfrac{1}{21}-\left(\dfrac{6-4}{21}\right)$$

$$=\dfrac{1}{21}-\dfrac{2}{21}$$

$$=\dfrac{1-2}{21}$$

$$=\dfrac{-1}{21}$$

Rahul bought $$1.5\ kg$$, Govind bought $$7.25\ kg$$ and Rakesh bought $$18\ kg$$ of wheat. What is the total quantity of wheat bought by them altogether?

Rahul bought=1.5 Kg

Govind bought

7.25 kg7.25 kg

Rakesh bought

18 kg18 kg

total quantity of wheat bought by them altogether=1.5+7.25+18=26.75Kg

Aneeta gave $$Rs. 2099.99$$ to her sister and $$Rs. 1991.11$$ to her brother. How much amount did she give in all?

amount she gave to her sister=2099.99

amount she gave to her brother=1991.11

total she gave=2099.99+1991.11

Rs 4091.1

Estimate the value of $$500+80+2+\dfrac{1}{10}+\dfrac{0}{100}+\dfrac{7}{1000}$$.

$$500+80+2+\dfrac{1}{10}+\dfrac{0}{100}+\dfrac{7}{1000}=500+80+2+0.1+0+0.007=582.107$$

Estimate the value of $$2000+0+70+3+\dfrac{2}{10}+\dfrac{6}{100}$$.

$$2000+0+70+3+\dfrac{2}{10}+\dfrac{6}{100}=2000+0+70+3+0.2+0.06=2073.26$$

Fill in the blank space.
19 + ____ = 42

Let 19 + x = 42

Therefore,

x = 42-19 = 23

Find the value of $$\dfrac {1}{2}+3 +\dfrac {1}{2}-3$$.

$$\dfrac{1}{2}+3+\dfrac{1}{2}-3=1-3+3=1$$

Simplify:-
$$4\frac{1}{2} - 1\frac{4}{5}$$

$$4\ 1/2-1\ 4/5$$

$$=\dfrac {(2)(4)+1}{2} \dfrac {(5)(1)+4}{5}$$

$$=\dfrac {9}{2}-\dfrac {9}{5}$$

$$=\dfrac {(9)(5)-(9)(2)}{(5)(2)}$$

$$=\dfrac {45-8}{10}$$

$$=\dfrac {27}{10}$$

$$=\dfrac {20}{10}+\dfrac {7}{10}$$

$$=2+\dfrac {7}{10}$$

$$=2\dfrac {7}{10}$$

Find the solution of the following:
$$(-9)+(+13)$$

$$(-9) + ( 13) $$

$$=-9+13$$

$$=4$$

How much is 90-19?

Given expression is $$90-19$$

The difference is $$90-19 = 71$$

Hence, $$90-19=71$$

The sum of the least number of three digits and largest number of two digits is .......

Least number of three digits is 100.

Largest number of two digits is 99.

Hence,

100 + 99 = 199 .

Solve :
  m cm
     $$5$$ $$12$$
+       $$3$$ $$46$$
_________________

$$5+3=8$$

$$12+46=58$$

$$\implies 8m58cm$$

Subtract:
(a) $$18$$ rupees $$9$$ paise from $$75$$ rupees $$80$$ paise.
(b) $$49$$ rupees $$79$$ paise from $$123$$ rupees $$68$$ paise.

(i) $$75.80$$

$$\underline { -18.09 } $$

$$57.71$$

$$=57$$ rupees $$71$$ paise

(ii) $$123.68$$

$$\underline { -49.79 } $$

$$73.89$$

$$\Rightarrow$$ $$73$$ rupees $$89$$ paise.

Simplify:
i) $$45 + (-12) - 12 $$
ii) $$123 + 89 - (-11)$$
iii) $$-85 - 15 + 200$$
iv) $$96 + (-16) - (-20) $$
v).$$ 36 - (-14) + 25 $$
vi) $$155 + (-25) + 50$$
vii) $$23 + (-56) - (-56) $$
viii) $$45 - 85 - 15 + (-25)$$
ix) $$78 - 39 + (-19) - (-29) $$
x) $$450 - 255 + (-230) + 560 $$

(i)

$$45+(-12)-12= 45-12-12$$

$$= 45-24$$

$$= 21$$

(ii)

$$123+89-(-11)= 123+89+11$$

$$=223$$

(iii)

$$-85-15+200=-100+200$$

$$=100$$

(iv)

$$96+(-16)-(-20)= 96-16+20$$

$$= 116-16$$

$$=100$$

(v)

$$36-(-14)+25= 36+14+25$$

$$=75$$

(vi)

$$155+(-25)+50= 155-25+50$$

$$= 205-25$$

$$= 180$$

(vii)

$$23+(-56)-(-56)= 23-56+56$$

$$= 79-56$$

$$= 23$$

(viii)

$$45-85-15+(-25)= 45-85-15-25$$

$$= 45-125$$

$$=-80$$

(ix)

$$78-39+(-19)-(-29)=75-39-19+29$$

$$= 104-58$$

$$=46$$

(x)

$$450-255+(-230)+560= 450-255-230+560$$

$$= 1010-485$$

$$=525$$

Solve :
$$(5+(-3)+6)$$

$$(5+(-3)+6)$$ = $$2+6$$ = $$8$$

Which is the largest $$3$$ digit number ?

Largest $$3$$ digit number is $$999$$.

Estimate $$5(10+1)$$

$$5(10+1)\\=5\times11\\=55$$

Find $$2+3$$

1206519_1244054_ans_d9714929084448079430621b3a5ec2de.jpg

PErform the give operation:
$$77+888$$
$$9999-1$$

$$77+888=965\\9999-1=9998$$

Find the value of $$48 ^ { 3 } - 30 ^ { 3 } - 18 ^ { 3 } $$.

$$48^3=48\times 48\times 48=110592\\30^3=30\times30\times30=27000\\18^3=18\times18\times18=5832\\48^3-30^3-18^3=110592-27000-5832=77760$$

Fill in.
In $$7362, 3$$ is in the__place and $$7$$ is in the place.

In $$7362, \; 3$$ is in the thousand place and $$7$$ is in the ten thousands place.

What does the $$b-a$$ represents in a number line?

The number $$b-a$$ is called the length of intervals $$\left(a,b\right),\left[a,b\right),\left(a,b\right],\left[a,b\right]$$

or distance between $$a$$ and $$b$$ on the number line.

What is $$1,00,00,000-1=?$$

$$ 100000000-1=$$ $$9999999$$.

Place commas correctly and write the numerals:
Nine crore five lakh forty one.

$$9,05,00,041$$.

Fill in the blank.
$$1$$ lakh $$=$$ _______ ten thousand.

$$1$$ lakh$$=\underline{10}$$ ten thousand.
($$1$$ lakh$$=1,00,000$$ and the thousand$$=10,000$$)

What is $$10-1=?$$

$$\textbf{Step 1: Using subtraction to get the value of required expression.}$$

$$10 - 1 = 9$$

$$\textbf{Hence, the required answer is 9.}$$

What is $$10,000-1=?$$

$$10000-1=9999$$.

What is $$100-1=?$$

$$100-1=99$$.

Fill in the blank.
$$1$$ million $$=$$_______ lakh.

$$1$$ million $$=\underline{10}$$lakh
($$1$$ million $$=1,000,000$$ and $$1$$ lakh$$=1,00,000$$)

Place commas correctly and write the numerals.
Seven crore fifty two-lakh twenty one thousand three hundred two.

$$7,52,21,302$$.

Place commas correctly and write the numerals:
Seventy three lakh seventy five thousand three hundred seven.

$$73,75,307$$.

How many $$7$$ -digit numbers are there in all ?

$$\textbf{Step-1: Write the least & greatest number of seven digits and simplify}$$

$$\Rightarrow$$ $$\text{The smallest}$$ $$7-$$ $$\text{digit number}$$ $$= 1000000.$$

$$\Rightarrow$$ $$\text{The greatest}$$ $$7-$$ $$\text{digit number}$$ $$= 9999999.$$

$$\Rightarrow$$ $$\text{Total}$$ $$4-$$ $$\text{digit numbers}$$ $$=(9999999 - 1000000)+1$$

$$\Rightarrow$$ $$89,99,999+1$$

$$=90,00,000$$

$$\text{So, we say that we have}$$ $$90,00,000$$ $$\text{seven-digit numbers.}$$

$$\textbf{Hence, answer is 90,00,000}$$

Insert commas suitably and write the names according to International System of Numeration:
$$7452283$$.

$$7,452,283$$
Seven million four hundred fifty two thousand two hundred eighty three.

Give a rough estimate(by rounding off to nearest hundreds) and also a closer estimate(by rounding off to nearest tens):
$$4,89,348-48,365$$.

$$4,89,348-48,365$$
Rounding off to hundreds, $$489348$$ and $$48365$$ may be rounded off to $$489300$$ and $$48400$$ respectively.
$$489300$$
$$-48400$$
__________
$$440900$$
__________
Rounding off to tens, $$489348$$ and $$48365$$ may be rounded off to $$489350$$ and $$48370$$ respectively.
$$489350$$
$$-48370$$
__________
$$440980$$
__________

Estimate the following using general rule.
$$12,904+2,888$$.

$$12904+2888$$
By rounding off to thousands, $$12904$$ rounds off to $$13000$$ and $$2888$$ rounds off to $$3000$$.
$$13000$$
$$+3000$$
__________
$$16000$$
__________

Give a rough estimate(by rounding off to nearest hundreds) and also a closer estimate(by rounding off to nearest tens):
$$439+334+4,317$$.

$$439+334+4317$$
Rounding off to nearest hundreds, $$439, 334$$ and $$4317$$ may be rounded off to $$400$$,
$$300$$ and $$4300$$ respectively.
$$400$$
$$300$$
$$+4300$$
________
$$5000$$
_________
Rounding off to nearest tens, $$439, 334$$ and $$4317$$ may be rounded off to $$440, 330$$ and $$4320$$ respectively.
$$440$$
$$330$$
$$+4320$$
________
$$5090$$
________

Round these numbers to the nearest tens.
$$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936$$.

$$28=30$$
$$32=30$$
$$52=50$$
$$41=40$$
$$39=40$$
$$48=50$$
$$64=60$$
$$59=60$$
$$99=100$$
$$215=220$$
$$1453=1450$$
$$2936=2940$$.

Estimate the following using general rule.
$$796-314$$.

$$796-314$$
By rounding off to hundreds, $$796$$ rounds off to $$800$$ and $$314$$ rounds off to $$300$$.
$$800$$
$$-300$$
__________
$$500$$
__________

Place commas correctly and write the numerals.
Twenty three lakh thirty thousand ten.

$$23,30,010$$.

Round off the given numbers to the nearest tens, hundreds and thousands.

$$75847$$ - Nearest Ten: $$75850$$
$$75847$$ - Nearest Hundred: $$75800$$
$$75847$$ - Nearest Thousand: $$76000$$
$$75847$$ - Nearest Ten Thousand: $$80000$$.

A bus started its journey and reached different places with a speed of $$60$$ km/hour. The journey is shown in given figure.

Find the total distance covered by the bus from A to D.

Total distance travelled by bus from A to D is equal to:-

$$=AB+BC+CD$$

$$=4170+3410+2160$$

$$=9740$$ km.

Insert commas suitably and write the names according to International System of Numeration:
$$78921092$$.

$$78,921,092$$
Seventy eight million nine hundred twenty one thousand ninety two.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign $$(>, <)$$ between them.
$$530$$, $$503$$.

$$530,503$$

As, $$530>503$$,

$$503$$ is on the left side of $$530$$ on the number line.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also written them with the appropriate sign $$(>, <)$$ between them.
$$98765$$, $$56789$$.

$$98765$$, $$56789$$
As $$98765 > 56789$$,
$$56789$$ is on the left side of $$98765$$ on the number line.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign $$(>, <)$$ between them.
$$370$$, $$307$$.

Step 1: To state

(1) Whole number which is on the left of the other number on the number line?

Step 2: Comparison

We have $$370$$, $$307$$ as whole numbers.
As $$370>307$$, therefore, $$307$$ is on the left side of $$370$$ on the number line.

Express the following numbers in standard form:
$$3908.78$$

$$3908.78=3.90878\times 1000=3.90878\times {10}^{3}$$

Write $$6789$$ correct to $$3$$ significant figures.

The correct number nearest to 6789 whose significant figure is 3 is $$6790$$

Write in Roman numerals.
$$92$$.

$$92- XCII$$.

Write in Roman numerals.
$$73$$.

$$73-LXXIII.$$

Write down, in figures, seventeen thousand and seventeen.

Seventeen thousand and seventeen $$= 17017$$

Write $$6789$$ correct to nearest $$100$$.

Nearest $$100$$ to $$6789$$ is $$6800$$

Round off the following number to nearest hundreds.
$$7,289$$.

1503144_1658556_ans_fa8b7918fd6f4f10b7e855dd4eb7f1bd.jpg

Write the roman-numerals for the following.
$$76$$.

For $$50$$ the roman numeral is $$L$$

Now for $$70$$ we have to move ahead $$20$$ so, we use $$XX$$

and for $$6$$ we know we have to add $$1$$ to $$5$$ so, $$VI$$

Hence, $$76=LXXVI$$

Write the roman-numerals for the following.
$$48$$.

1504306_1658749_ans_05d01df824ad4fae96754786d00af110.jpg

Round off the following number to nearest hundreds.
$$4,20,387$$.

1503148_1658562_ans_1dcc332f529d426cba3059d66fc85d00.jpg

Round off the following number to the nearest thousand.
$$20,963$$.

20963 is nearer to 21000 than 20000.

So, answer is 21000.

Write the following in Roman numerals.
$$154$$.

We know that the roman numeral for $$100$$ is $$=C$$

and for $$50$$ it is $$=L$$

Now, to add $$4$$ more we can subtract $$1$$ from $$5$$ i.e $$=IV$$

So, $$154=CLIV$$

Estimate the following by rounding off the number to its greatest place.
$$1,08,734-47,599$$.

1671905_1658611_ans_0c5f2e2a4c85498fa5e9efd1ae3bb262.JPG

Estimate the following by rounding off the number to its greatest place.
$$9\times 795$$.

1573128_1658615_ans_3df7f6b976e24bf9b1ff2a4023d0fe6e.jpg

Round off the following number to nearest hundreds.
$$14,627$$.

At the $$10th$$ place the number is $$2$$ which is less than $$5$$
$$\therefore14,627$$ is nearer to hundred is $$14,600$$
So, answer is $$14,600$$

Round off the following number to nearest hundreds.
$$8,074$$.

1503145_1658557_ans_23c7d9d0df7d479da2ac33f8daff5261.jpg

Estimate the following by rounding off the number to its greatest place.
$$87\times 317$$.

1573130_1658616_ans_6ced81fd6e6841a1873912834721c6fd.jpg

Fill in the blank with the appropriate symbol $$<$$ or $$>$$.
$$170$$____$$107$$.

$$170$$ is more than $$107$$
$$\therefore 170>107$$

Estimate the difference to the nearest thousand:
$$(47005 - 39488)$$

Estimated value to the nearest thousands of $$47005 = 47000$$

Estimated value to the nearest thousands of $$39488 = 39000$$

$$\therefore$$ required estimation $$= (47000 - 39000) = 8000$$

Round the following number to the nearest thousand:
$$28394$$

Here $$3$$ is in hundred digits place
$$3 < 5$$
$$\therefore$$ required rounded number is $$28000$$

Round the following number to the nearest ten thousand:
$$17514$$

Thousand digits number is $$7 > 5$$
$$\therefore$$ required number is $$20000$$

Estimate the difference to the nearest thousand:
$$(35863 - 27677)$$

Estimated value to the nearest thousands of $$35863 = 36000$$

Estimated value to the nearest thousands of $$27677 = 28000$$

$$\therefore$$ required estimation $$= (36000 - 28000) = 8000$$

Express the following as a Roman numeral:
$$2$$

Roman number of $$2$$ is written as $$II$$

Write the following in Roman numerals.
$$319$$.

1504316_1658755_ans_83bfd33c316044c9923ebcd900477237.jpg

$$100$$ thousands$$=$$ ______ lakh.

$$100$$ thousands $$=100,000=1$$ followed by $$5$$ zeros$$=1$$ lakh.

Arrange the following numbers in descending order:
$$8435,\ 4835,\ 13584,\ 5384,\ 25843$$

The descending order of the given numbers is :

$$25843>13584>8435>5348>4835$$

$$10$$ lakh $$=$$____ million.

$$1$$ million is the number which can be written as $$1$$ followed by $$6$$ zeros

$$10\ lakh =10,00,000\\=1,000,000\\=1\ milion$$

$$1$$ kilometre $$=$$ _____ millimetres.

$$1$$ kilometre $$=1000000$$ metres

$$1$$ centimetre $$=$$ _____ millimetres.

$$1$$ centimetre $$=10$$ millimetres

Write the following decimal in expanded form:
$$4615.72 $$

$$ 4615.72 $$
$$= 4$$ thousands $$+ 6$$ hundreds $$+1$$ tens $$+5$$ ones $$+7$$ tenths $$+2$$ hundredths

$$= (4\times 1000)+(6\times 100)+(1\times 10)+(5\times 1)+(7\times \dfrac{1}{10})+(2\times \dfrac{1}{100}) $$

$$= 4000+600+10+5+\dfrac{7}{10}+\dfrac{2}{100} $$

$$ \therefore $$ $$ 4615.72 = 4000+600+10+5+\dfrac{7}{10}+\dfrac{2}{100} $$

$$1$$ meter $$=$$ _____ millimetres.

$$1$$ meter $$=1000$$ millimetres.

$$1$$ gram $$=$$ ______ milligrams.

$$1$$ gram $$=1000$$ milligrams.

$$1$$ liter $$=$$ ______ millilitres.

$$1$$ liter $$=1000$$ millilitres.

$$1$$ kilogram $$=$$ ______ milligrams.

$$1$$ kilogram $$=10,00,000$$ milligrams.

Estimate each of the following by rounding off each number to nearest tens:
$$10732-4354$$

Nearest ten's round off $$10732$$ is $$10730$$ and round off $$4354$$ is $$4350$$

So, rounded the total nearest is $$=10730-4350=6380$$

Find the smallest and the greatest numbers in each case given below:
$$983, 5754, 84$$ and $$5942$$

Since $$84$$ has the least number of digits.
$$84$$ is the least smallest
$$5754$$ and $$5942$$ have the maximum number of digits. $$5942$$ is greater than $$5754$$
Therefore $$84$$ is the smallest number and $$5942$$ is the greatest number

By making a suitable chart, compare:
$$540276$$ and $$369998$$

$$5$$ $$4$$ $$0$$ $$2$$ $$7$$ $$6$$

$$3$$ $$6$$ $$9$$ $$9$$ $$9$$ $$8$$

Here, both the numbers have equal number of digits $$i.e. 6$$

At the leftmost, the first number has $$5$$ and the second number has $$3$$

Since $$ 5 > 3$$

$$540276$$ is greater than $$369998$$

By making a suitable chart, compare:
$$6983245$$ and $$6893254$$

$$6$$ $$9$$ $$8$$ $$3$$ $$2$$ $$4$$ $$5$$

$$6$$ $$8$$ $$9$$ $$3$$ $$2$$ $$5$$ $$4$$

Here, both the numbers have equal number of digits $$i.e. 7$$

At the leftmost, both the numbers have the same digit $$i.e. 6$$

At the second place from left, the first number has $$9$$ and the second number has $$8$$

Since, $$ 9 > 8$$

$$6983245$$ is greater than $$6893254$$

$$P$$ liters = ________ mililiters.

1888089_1789780_ans_41b94fca5ffb456881f91ea8d58530a9.jpg

Estimate each of the following by rounding off each number to nearest tens:
$$78203-16407$$

Nearest ten's round off $$78203$$ is $$78200$$ and round off $$16407$$ is $$16410$$

So, rounded the total nearest is $$=78200-16410=61790$$

Estimate each of the following by rounding off each number to nearest tens:
$$76877-7783$$

Nearest ten's round off $$76877$$ is $$76880$$ and round off $$7783$$ is $$7780$$

So, rounded the total nearest is $$=76880-7780=69100$$

The height of a person is $$1\ m\ 65\ cm$$. His height in millimetres is _________.

We know that,

$$1\ m=1000\ mm$$ and $$1\ cm =10 \ mm$$

$$\therefore 1\ m\ 65\ cm= (1000\ mm)+(65\times10\ mm)\\=(1000+650)\ mm=1650\ mm$$

Hence, the height of the person in millimetre is $$1650\ mm.$$

Estimate each of the following by rounding off each number to nearest hundreds:
$$793+397$$

Nearest hundreds round off $$739$$ is $$800$$ and round off $$397$$ is $$400$$
So, rounded the total nearest is $$=800+400=1200$$

Round off each of the following to the nearest ten: $$62$$

If the one's place digit is less than $$5$$, replace one's place digit by $$0$$, and keep the other digit as the same and if the digit at ones place is $$5$$ or more than $$5$$, increase tens digit by $$1$$ and replace ones digit by $$0$$.

$$62$$ to the nearest ten is $$60$$

Round off each of the following to the nearest ten: $$265$$

If the ones place digit is less than $$5$$, replace ones digit by $$0$$, and keep the other digit as the same. And if the digit at ones place is $$5$$ or more than $$5$$, increase tens digit by $$1$$ and replace ones digit by $$0$$.
$$265$$ to the nearest ten is $$270$$.

Round off each of the following to the nearest ten: $$8261$$

Round off each of the following to the nearest ten: $$6294$$

Round off each of the following to the nearest hundred: $$2667$$.

If the digit at tens place is less than $$5$$, replace each one of tens and ones digits by $$0$$ and keep the other digits as the same.
If the tens digit is $$5$$ or more than $$5$$, increase the hundreds digit by $$1$$ and replace each of tens and ones digit by $$0$$
$$2667$$ to the nearest hundred is $$2700$$.

Round off each of the following to the nearest ten: $$543$$

Round off each of the following to the nearest hundred: $$784$$

Find the smallest and the greatest numbers in each case given below:
$$32849, 53628, 5499$$ and $$54909.$$

Since $$5499$$ has the least number of digits.
$$5499$$ is the smallest
$$54909$$ and $$53628$$ have the maximum number of digits. Among these two $$54909$$ is the greater than $$53628$$
Therefore $$5499$$ is the smallest number and $$54909$$ is the greatest number

Round off each of the following to the nearest hundred: $$748$$

Round off each of the following to the nearest hundred: $$5432$$.

Round off each of the following to the nearest thousand: $$9248$$.

Observe the hundreds digit of the given number.
If the hundreds digit is less than $$5$$, replace each one of hundreds, tens, and ones digits by $$0$$ and keep the other digits as same.
If hundreds digit is $$5$$ or more than $$5$$ in the given number, increase thousand digit by $$1$$ and replace each other digit on its right by $$0$$.
$$9248$$ to the nearest thousand is $$9000$$.

Round off $$6732$$ to the nearest thousand.

Round off $$4327$$ to the nearest thousand.

since $$3$$ is less than $$5$$, therefore nearest to thousand is $$4000$$
Hence, $$4327$$ to the nearest thousand is $$4000$$.

Round off each of the following to the nearest thousand: $$25352$$.

Round off each of the following to the nearest thousand: $$32568$$.

Round off $$578$$ to the nearest ten.

Round off $$32974$$ to the nearest ten-thousand.

$$32974$$ to the nearest ten-thousand is $$30000$$.

Round off $$578$$ to the nearest hundred.

We see the digit in the tens place is $$7,$$ we round to the nearest multiple of hundred which is greater than the number. Hence, $$578$$ is nearer to $$600$$ than $$500.$$

$$578$$ to the nearest hundred is $$600$$.

Round off each of the following to the nearest thousand: $$6475$$.

Round off each of the following to the nearest hundred: $$6388$$.

Round off each of the following to the nearest ten, nearest hundred and nearest thousand: $$1249$$.

$$1249$$ to the nearest ten is $$1250$$,
$$1249$$ to the nearest hundred is $$1200$$,
$$1249$$ to the nearest thousand is $$1000$$.

Round off each of the following to the nearest ten, nearest hundred and nearest thousand: $$54, 547$$

$$54547$$ to the nearest ten is $$54550$$,
$$54547$$ to the nearest hundred is $$54500$$,
$$54547$$ to the nearest thousand is $$55000$$.

Round off each of the following to the nearest ten, nearest hundred and nearest thousand: $$56,293$$.

$$56293$$ to the nearest ten is $$56290$$,
$$56293$$ to the nearest hundred is $$56300$$,
$$56293$$ to the nearest thousand is $$56000$$.

Round off each of the following to the nearest ten, nearest hundred and nearest thousand: $$68,076$$.

$$68076$$ to the nearest ten is $$68080$$,
$$68076$$ to the nearest hundred is $$68100$$,
$$68076$$ to the nearest thousand is $$68000$$.

Round off the following to the nearest tens: $$562$$.

Round off the following to the nearest tens: $$545 cm$$.

$$545 cm$$ to the nearest ten is $$550 cm$$.

Round off $$27487$$ to the nearest ten-thousand.

$$27487$$ to the nearest ten- thousand is $$30000$$. As the thousand digit of the given number is $$7$$ that is greater than $$5$$ so, we will increase the ten-thousand digit by $$1$$ and rest all digit will become $$0.$$

Round off the following to the nearest tens: $$837 m$$.

Round off each of the following to the nearest ten, nearest hundred and nearest thousand: $$864$$.

$$864$$ to the nearest ten is $$860$$,
$$864$$ to the nearest hundred is $$900$$,
$$864$$ to the nearest thousand is $$1000$$.

List all the numbers which can be round off to $$30$$.

$$26, 27, 28, 29,31, 32, 33, 34$$ are the numbers that can be rounded off to $$30$$.

Estimate the sum of each pair of numbers to the nearest ten: $$96$$ and $$55$$.

$$96$$ to the nearest ten is $$100$$,
$$55$$ to the nearest ten is $$60$$,
Sum of these numbers = $$100 + 60 = 160$$.
$$\therefore$$ Required sum = $$160$$.

Estimate the sum of each pair of numbers to the nearest hundred: $$336$$ and $$782$$.

$$336$$ to the nearest hundred is $$300$$
and $$782$$ to the nearest hundred is $$800$$,
Sum of these numbers = $$(300 + 800) = 1100$$.
$$\therefore$$ Required sum = $$1100$$.

Write the smallest and the largest numbers which are rounded off to $$80$$.

$$75$$ is the smallest number which is rounded off to $$80$$
and $$84$$ is the largest number which is rounded off to $$80$$.

Estimate the sum of each pair of numbers to the nearest ten: $$23$$ and $$66$$.

$$23$$ to the nearest ten is $$20$$,
$$66$$ to the nearest ten is $$70$$,
Sum of these numbers = $$20 + 70 = 90$$.
$$\therefore$$ Required sum = $$90$$.

Write the smallest and the largest numbers which are rounded off to $$130$$.

$$125$$ is the smallest number which is rounded off to $$130$$
and $$134$$ is the largest number which is rounded to off to $$130$$.

Estimate the sum of each pair of numbers to the nearest hundred: $$546$$ and $$342$$.

$$546$$ to the nearest hundred is $$500$$
and $$342$$ to the nearest hundred is $$300$$,
Sum of these numbers = $$(500 + 300) = 800$$.
$$\therefore$$ Required sum = $$800$$.

Estimate the sum of each pair of numbers to the nearest ten: $$78$$ and $$18$$.

$$78$$ to the nearest ten is $$80$$,
$$18$$ to the nearest ten is $$20$$,
Sum of these numbers = $$80 + 20 = 100$$.
$$\therefore$$ Required sum = $$100$$.

Estimate the sum of each pair of numbers to the nearest ten: $$67$$ and $$44$$.

$$67$$ to the nearest ten is $$70$$,
$$44$$ to the nearest ten is $$40$$,
Sum of these numbers = $$70 + 40 = 110$$.
$$\therefore$$ Required sum = $$110$$.

Estimate the sum of each pair of numbers to the nearest ten: $$34$$ and $$87$$.

$$34$$ to the nearest ten is $$30$$,
$$87$$ to the nearest ten is $$90$$,
Sum of these numbers = $$30 + 90 = 120$$.
$$\therefore$$ Required sum = $$120$$.

List all the numbers which can be rounded off to $$50$$.

$$45,46, 47, 48, 49, 51, 52, 53, 54$$ are the numbers that can be rounded off to $$50$$.

Estimate the following differences correct to nearest ten: $$96 – 36$$.

$$96$$ to the nearest ten is $$100$$ and $$36$$ to the nearest ten is $$40$$,
$$\therefore$$ Required difference = $$(100 – 40) = 60$$.

Estimate each difference to the nearest hundred: $$769$$ - $$314$$.

$$769$$ to the nearest hundred = $$800$$, and
$$314$$ to the nearest hundred = $$300$$,
$$\therefore$$ Required difference = $$(800 – 300) = 500$$.

Estimate the sum of each pair of numbers to the nearest hundred: $$4230$$ and $$2410$$.

$$4230$$ to the nearest hundred is $$4200$$
and $$2410$$ to the nearest hundred is $$2400$$,
Sum of these numbers = $$(4200 + 2400) = 6600$$.
$$\therefore$$ Required sum = $$6600$$.

Estimate the sum of the following pair of numbers to the nearest thousand: $$53826$$ and $$36455$$.

$$53826$$ to the nearest thousand is $$54000$$,
$$36455$$ to the nearest thousand is $$36000$$,
$$\therefore$$ Required sum = $$54000 + 36000 = 90000$$.

Estimate the following differences correct to nearest ten: $$508$$ - $$248$$.

$$508$$ to the nearest ten is $$510$$ and $$248$$ to the nearest ten is $$250$$,
$$\therefore$$ Required difference = $$(510 – 250) = 260$$.

Estimate the sum of each pair of numbers to the nearest hundred: $$4280$$ and $$5295$$.

$$4280$$ to the nearest hundred is $$4300$$ and $$5295$$ to the nearest hundred is $$5300$$,
Sum of these numbers = $$(4300 + 5300) = 9600$$.
$$\therefore$$ Required sum = $$9600$$.

Estimate the following differences correct to nearest ten: $$82 – 27$$.

$$82$$ to the nearest ten is $$80$$ and $$27$$ to the nearest ten is $$30$$,
$$\therefore$$ Required difference = $$(80 – 30) = 50$$.

Estimate each difference to the nearest hundred: $$856$$ $$687$$.

$$856$$ to the nearest hundred = $$900$$, and
$$687$$ to the nearest hundred = $$700$$,
$$\therefore$$ Required difference = $$(900 – 700) = 200$$.

Estimate the sum of each pair of numbers to the nearest hundred: $$270$$ and $$495$$.

$$270$$ to the nearest hundred is $$300$$
and $$495$$ to the nearest hundred is $$500$$,
Sum of these numbers = $$(300 + 500) = 800$$.
$$\therefore$$ Required sum = $$800$$.

Estimate the sum of the following pair of numbers to the nearest thousand: $$56802$$ and $$22475$$.

$$56802$$ to the nearest thousand is $$57000$$,
$$22475$$ to the nearest thousand is $$22000$$,
$$\therefore$$ Required sum $$=57000 + 22000$$

$$ = 79000$$.

Estimate each of the following products by rounding off each number to the nearest ten: $$49\times52$$.

$$49$$ to the nearest ten = $$50$$, and
$$52$$ to the nearest ten = $$50$$,
$$\therefore$$ Required product = $$(50 \times50) = 2500$$.

Estimate each difference to the nearest thousand: $$76003$$ $$48399$$.

$$76003$$ to the nearest thousand = $$76000$$,
$$48399$$ to the nearest thousand = $$48000$$,
$$\therefore$$ Required difference = $$(76000 – 48000) = 28000$$.

Estimate each difference to the nearest thousand: $$45974$$ $$38766$$.

$$45974$$ to the nearest thousand = $$46000$$,
$$38766$$ to the nearest thousand = $$39000$$,
$$\therefore$$ Required difference = $$(46000 – 39000) = 7000$$.

Estimate each of the following products by rounding off each number to the nearest hundred: $$624 \times 236$$.

$$624 \times 236$$
$$624$$ to the nearest hundred = $$600$$, and
$$236$$ to the nearest hundred = $$200$$,
$$\therefore$$ Required product = $$(600 \times 200) = 120,000$$.

Estimate each of the following products by rounding off each number to the nearest ten: $$27 \times 54$$.

$$27$$ to the nearest ten = $$30$$, and
$$54$$ to the nearest ten = $$50$$,
$$\therefore$$ Required product = $$(30 \times 50) = 1500$$.

Estimate each of the following products by rounding off each number to the nearest ten: $$53 \times 85$$.

$$53$$ to the nearest ten = $$50$$, and
$$85$$ to the nearest ten = $$90$$,
$$\therefore$$ Required product = $$(50 \times 90) = 4500$$.

Estimate each of the following products by rounding off each number to the nearest ten: $$63 \times 38$$.

$$63$$ to the nearest ten = $$60$$, and
$$38$$ to the nearest ten = $$40$$,
$$\therefore$$ Required product = $$(60 \times 40) = 2400$$.

Estimate each of the following products by rounding off each number to the nearest hundred: $$477\times213$$.

$$477 \times 213$$
$$477$$ to the nearest hundred = $$500$$, and
$$213$$ to the nearest hundred = $$200$$,
$$\therefore$$ Required product = $$(500 \times 200) = 100,000$$.

Estimate each of the following products by rounding off each number to the nearest ten: $$74 \times 67$$.

$$74$$ to the nearest ten = $$70$$, and
$$67$$ to the nearest ten = $$70$$,
$$\therefore$$ Required product = $$(70 \times 70) = 4900$$.

Estimate each difference to the nearest hundred: $$6352$$ $$2086$$.

$$6352$$ to the nearest hundred = $$6400$$, and
$$2086$$ to the nearest hundred = $$2100$$,
$$\therefore$$ Required difference = $$(6400 – 2100) = 4300$$.

Estimate each of the following products by rounding off each number to the nearest hundred: $$537 \times 283$$.

$$537 \times 283$$
$$537$$ to the nearest hundred = $$500$$, and
$$283$$ to the nearest hundred = $$300$$,
$$\therefore$$ Required product = $$(500 \times 300) = 150,000$$.

Write the following numbers, placing the commas, according to International System:
$$428140584=$$.........

Numbers placing the commas, according to International system are $$428140584=428,140,584$$

Add (giving answer in metre):
$$2.4 m$$ and $$1.78 m$$

$$2.4 m$$ and $$1.78 m$$
$$2.40 m$$
$$1.78 m +$$
_________
$$4.18 m$$
_________
$$\therefore$$ The addition of $$2.4 m$$ and $$1.78 m = 4.18 m$$

Estimate each of the following products by rounding off each number to the nearest hundred: $$333 \times 247$$.

$$333 \times 247$$
$$333$$ to the nearest hundred = $$300$$, and
$$247$$ to the nearest hundred = $$200$$,
$$\therefore$$ Required product = $$(300 \times 200) = 60,000$$.

Estimate each of the following products by rounding off each number to the nearest hundred: $$382 \times 127$$.

$$382 \times 127$$
$$382$$ to the nearest hundred = $$400$$, and
$$127$$ to the nearest hundred = $$100$$,
$$\therefore$$ Required product = $$(400 \times 100) = 40,000$$.

Write the following numbers, placing the commas, according to International System:
$$63560981=$$.........

Numbers placing the commas, according to International system are $$63560981=63,560,981$$

In the number of $$ 40562, $$ the sum of the place value of $$ 5 $$ and the place value of $$ 6 $$ = .........

The sum of the place value of $$ 5 $$ and the place value of $$ 6 = 500 + 60 = 560 $$

Estimate each of the following products by rounding off the first number correct to nearest ten and the other number correct to nearest hundred: $$432 \times 128$$.

$$432 \times 128$$
$$432$$ to the nearest ten = $$430$$, and
$$128$$ to the nearest ten = $$100$$,
$$\therefore$$ Required product = $$(430 \times 100) = 43,000$$.

Estimate each of the following products by rounding off the first number correct to nearest ten and the other number correct to nearest hundred: $$28 \times 287$$.

$$28 \times 287$$
$$28$$ to the nearest ten = $$30$$, and
$$287$$ to the nearest ten = $$300$$,
$$\therefore$$ Required product = $$(30 \times 300) = 9,000$$.

Write the following numbers, placing the commas, according to Indian System:
$$835629=$$.........

Numbers placing the commas, according to International system are
$$6509823=6,509,820$$

Estimate the following using general rule:
$$12,904 + 2,888$$

$$12,904 + 2,888 :-$$

By rounding off to thousands, $$12904$$ rounds off to $$13000$$ and $$2822$$ round off to $$3000$$

$$13000$$

$$+3000$$

$$........$$

Total $$16000$$

The addition of these two number is $$16,000.$$

Fill in the blanks:-
$$1$$ million = __ hundred thousand

$$1,000,000=10\times100,000$$

$$1$$ million = $$10$$ hundred thousand

Fill in the blanks:-
$$1$$ lakh = __ ten thousand.

$$1,00,000=10\times10,000$$

$$1$$ lakh = $$10$$ ten thousand.

Fill in the blanks:-
$$1$$ crore = __ ten lakh

$$1,00,00,000=10\times 10,00,000$$

$$1$$ crore = $$10$$ ten lakh

Estimate the following using general rule:
$$796 - 314$$

$$796 - 314$$

By rounding off to hundreds, $$796$$ rounds off to $$800$$ and $$314$$ rounds off to $$300$$

$$800$$ $$-300=500$$

Total $$500$$

The difference of these two number is $$500$$.

Add (giving answer in metre):
$$848 cm$$ and $$2.9 m$$

$$848 cm$$ and $$2.9 m$$
$$= 848 / 100 m + 2.9 m$$ $$\left \{ 1 m = 100 cm \right \}$$
$$= 8.48 m + 2.9 m$$
$$8.48$$
$$2.9 +$$
___________
$$11.38$$
____________
$$\therefore$$ The addition of $$848 cm$$ and $$2.9 m = 11.38 m$$

Write :
$$63521769$$ correct to the nearest hundred.

If the number you are rounding is followed by $$5, 6, 7, 8$$ or $$9$$ round the number up to $$10$$.

Example: $$38$$ rounded to the nearest ten is $$40$$.

here, $$69$$ rounded to $$70$$

Ans:- $$63521770$$

The ages in years of $$10$$ teachers of a school are-
$$32, 41, 28, 54, 35, 26, 23, 33, 38, 40$$
What is the age of the oldest teacher and that of the youngest teacher?

Arranging the ages in ascending order, we get-
$$23, 26, 28, 32, 33, 35, 38, 40, 41, 54$$
We find that the age of the oldest teacher is $$54$$ years and the age of the youngest teacher is $$23$$ years.

Find the number for given roman number
CLXVI = __________.

Given that, $$CLXVI$$.

We know that,

$$CLXVI=166$$

Hence, this is the answer.

Add together $$2321,4032,300421$$ in the scale of five.

When the digits are added any no. greater than or equal to $$5$$ is converted, E.g.,

$$7=5\times 1+2$$

$$8=5\times 1+3$$

In the scale of eight subtract $$371532$$ from $$530225$$, and multiply the difference by$$27$$

$$530225$$
$$371532$$
---------------
$$136473$$

$$136473$$
$$27$$
_________
$$1226235$$
$$275166$$
_________
$$4200115$$

After the first figure of the subtraction, since we cannot take $$3$$ from $$2$$ we add $$8$$; thus we have to take $$3$$ from ten, which leaves $$7$$; then $$6$$ from ten, which leaves $$4$$; then $$2$$ from eight which leaves $$6$$; and so on.
Again, in multiplying by $$7$$, we have
$$3\times 7=$$ twenty one $$=2\times 8+5$$;
we therefore put down $$5$$ carry $$2$$.
Next $$7\times 7+2=$$ fifty one $$=6\times 8+3$$;
put down $$3$$ and carry $$6$$; and so on, until the multiplication is completed
In addition,
$$3+6=$$ nine $$=1\times 8+1$$;
we therefore put down $$1$$ and carry $$1$$.
Similarly $$2+6+1=$$ nine $$=1\times 8+1$$;
and $$6+1+1=$$ eight $$=1\times 8+0$$;
and so on.

Solve: $$ \dfrac{21}{20} + \left (- \dfrac{19}{30}\right)$$

$$\dfrac{21}{20}+\left(-\dfrac{19}{30}\right)=\dfrac{21}{20}-\dfrac{19}{30}$$

$$=\dfrac{1}{10}\left(\dfrac{21}{2}-\dfrac{19}{3}\right)$$

$$=\dfrac{1}{10}\left(\dfrac{63-38}{6}\right)$$

$$=\dfrac{1}{10}\left(\dfrac{25}{6}\right)$$

$$=\dfrac{5}{12}$$

Solve $$(-8)+(-5)+(+6)$$

given

$$(-8)+(-5)+(+6)$$

$$\Rightarrow (-8)+(-5)+(+6)=-8-5+6=-7$$

Vedika has $$23.50$$ meters of cloth. She used it to make $$5$$ curtains of equal size . if each curtain required $$4$$ meters $$25cm$$ to make, how much cloth is left over?

Length of cloth vedika has $$23.50$$ m

No. if same size curtains she made $$=5$$

length of each curtains $$= 4m $$ $$25cm$$

Total cloth used $$= 5 \times 4 m$$ $$25cm$$

$$=21m$$ $$25cm$$

cloth left with her $$=23.50 -21.25$$

$$=2m$$ $$25cm$$

Solve $$(-5)+(+4)+(-1)$$

given

$$(-5)+(+4)+(-1)$$

$$\Rightarrow (-5)+(+4)+(-1)=-5+4-1=-2$$

The length of one rod is $$2.53cm$$ and that of the other is $$1.27 cm$$. The least count of the measuring instrument is $$0.01$$cm. If the two rods are put together end to end, find the combined length.

Since, the Least count is $$0.01$$

we can directly add the $$2$$ lengths

$$\Rightarrow 2.53+1.27=2.00+0.53+1.00+0.27=2+1+0.80=3.80\ cm$$

Solve $$(-22)-(+12)$$

given equation is

$$(-22)-(+12)$$

$$\Rightarrow (-22)-(+12)=-22-12=-34$$

Solve $$(+9)-(+4)$$

$$\textbf{Step1-Find difference of given integers}$$

$$ (+9)-(+4)=9-4$$

$$\Rightarrow (+9)-(+4)=5$$

$$\textbf{Sum of (+9)-(+4) is equal to 5}$$

Solve $$(+11)-(+4)$$

given equation is

$$(+11)-(+4)$$

$$\Rightarrow (+11)-(+4)=11-4=7$$

Solve $$(-4)-(+14)$$

given equation is

$$(-4)-(+14)$$

$$\Rightarrow (-4)-(+14)=-4-14=-18$$

Solve $$(-6)-(+3)$$

given equation is

$$(-6)-(+3)$$

$$\Rightarrow (-6)-(+3)=-6-3=-9$$

Solve $$(-9)-(-15)$$

given equation is

$$(-9)-(-15)$$

$$\Rightarrow (-9)-(-15)=-9+15=6$$

Solve $$(+13)-(+4)$$

given equation is

$$(+13)-(+4)$$

$$\Rightarrow (+13)-(+4)=13-4=9$$

Solve $$(+12)-(+5)$$

given equation is

$$(+12)-(+5)$$

$$\Rightarrow (+12)-(+5)=12-5=7$$

Solve $$(+5)-(3)$$

given equation is

$$(+5)-(3)$$

$$\Rightarrow (+5)-(3)=5-3=2$$

Solve $$(+4)-(+6)$$

given equation is

$$(+4)-(+6)$$

$$\Rightarrow (+4)-(+6)=4-6=-2$$

$$12(2x-5)+3x=81$$

given equation is

$$12(2x-5)+3x=81$$

$$\Rightarrow 12(2x-5)+3x=24x-60+3x=81$$

$$\Rightarrow 27x=81+60=141$$

therefore $$x=\dfrac{141}{27}=\dfrac{47}{9}$$

A number, when rounded off to the nearest ten thousand, has rounded-off value of $$30,000$$. What is the possibility of that number?

It can be any number between $$25,001$$ to $$35,499$$ inclusively.

Write the following Roman numerals in the Hindu-Arabic system.
a) IV b) IX c) XII
d) XVI e) XXX f) XL
g) XXV h) XLI i) XLI

$$a) IV = 4 $$

$$b) IX = 6$$

$$c) XII = 12$$

$$d) XVI =16$$

$$e) XXX = 30 $$

$$f) XL = 40$$

$$g) XXV = 25$$

$$h) XLI = 41$$

$$i) XLI =41$$

Solve the given expression:

$$\cfrac{10.25+9+4.75+8+2.65+12+2.35}{7}$$

Given: $$\cfrac{10.25+9+4.75+8+2.65+12+2.35}{7}$$

$$=\cfrac{49}{7}$$

$$=7$$

If the sum of the reciprocals of two consecutive positive numbers is $$\dfrac{21}{110}$$ then find the numbers.

Let the two consecutive positive numbers be $$x$$ and $$x+1$$.

Then according to the problem,

$$\dfrac{1}{x}+\dfrac{1}{x+1}=\dfrac{21}{110}$$

or, $$\dfrac{2x+1}{x(x+1)}=\dfrac{21}{110}$$

or, $$220x+110=21x^2+21x$$

or, $$21x^2-199x-110=0$$

or, $$21x^2-210x+11x-110=0$$

or, $$21x(x-10)+11(x-10)=0$$

or, $$(x-10)(21x+11)=0$$

or, $$x=10$$. [ Since $$x$$ is positive]

So the numbers are $$10,11$$.

Add $$4{ x }^{ 2 }-7xy+4{ y }^{ 2 }-3$$,
$$5+6{ y }^{ 2 }-8xy+{ x }^{ 2 }$$

$$4{ x }^{ 2 }-7xy+4{ y }^{ 2 }-3+5+6{ y }^{ 2 }-8xy+{ x }^{ 2 }$$

$$=5{ x }^{ 2 }+10{ y }^{ 2 }-15xy+2$$

$$=5{ x }^{ 2 }-5xy-10xy+10{ y }^{ 2 }+2$$

$$=5x(x-y)-10y(x-y)+2$$

$$=5(x-2y)(x-y)+2$$

Subtract $$\rightarrow -6p+q+3r+8$$ from $$p-2q-5r-s$$

$$\Rightarrow p-2q-5r-8-\left( -6p+q+3r+8 \right) $$

$$=p-2q-5r-8+6p-q-3r-8$$

$$=7p-3q-8r-16$$

Solve $$(-4)-(-11)$$

given equation is

$$(-4)-(-11)$$

$$\Rightarrow (-4)-(-11)=-4+11=7$$

Solve $$(-3)-(-12)$$

given equation is

$$(-3)-(-12)$$

$$\Rightarrow (-3)-(-12)=-3+12=9$$

Use the sign $$>, <, =$$ fill in the blanks$$\left( -8 \right) +\left( -4 \right) \Box \left( -8 \right) -\left( -4 \right) $$

The given expression is $$\left( { - 8} \right) + \left( { - 4} \right)\ \square\left( { - 8} \right) - \left( { - 4} \right)$$

$$ - 8 - 4\ \square - 8 + 4$$

$$ - 12\ \square- 4$$

Since, $$ - 12$$ is less than $$ - 4$$, therefore,

$$ - 12 < - 4$$

Calculate the next time and mention it using a.m. or p.m.
(i) 20 minutes after 6:05 p.m. =
(ii) 5 minutes after 2:10 a.m.=
(iii) 40 minutes after 10:30 a.m.=
(iv) 15 minutes after 12 midnight =
(v) 45 minutes after 4:30 p.m.=
(vi) 30 minutes after 7:35 a.m.=

$$20$$ minutes after $$6:05pm=6:25pm$$

$$5$$ minutes after $$2:10am=2:15am$$

$$40$$ minutes after $$10:30am=11:10am$$

$$15$$ minutes after $$12$$ midnight$$=12:15am$$

$$45$$ minutes after $$4:30pm=5:15pm$$

$$30$$ minutes after $$2:35am=8:05am$$

Express the following numbers in standard form:
$$70,500,000$$

$$70,500,000 = 705\times 10^{5}$$.

$$=7.05\times 10^{7}$$ Ans

The sum of three consecutive even numbers is $$54$$. Find the numbers.

Sum of three consecutive integers can be written as. $$(a−1)+a+(a+1)=54$$. or. $$3a-1+1=54$$. or. $$3a+0=54$$. or. $$3a=54$$. or. $$a=54/3$$. $$a$$=$$18$$
$$a−1$$.
$$=18-1$$ =$$17$$ ========Ans $$1$$.
$$a$$=$$18$$ Ans 2.
and $$a+1$$.
$$=18+1=19$$ ========Ans $$3$$.

How much is 190-87+16 ?

190-87+16 = 103+16 =119

Round off each of the following numbers to the nearest hundred, thousand ten thousand and lakh.
$$85364$$

$$\rightarrow$$ Given number : $$85364$$

Rounding off to nearest hundred : $$85,400$$

Rounding off to nearest thousand : $$85,000$$

Rounding off to nearest ten thousand : $$90000$$

Rounding off to nearest lakh : $$1,00000$$

If $$a = 2$$ and $$b = 3$$, find the value of $$ab - a^{2}$$.

$$\textbf{Step 1 : Given information,}$$

$$\text{Given that, }a=2,b=3$$

$$\text{Expression is}=ab-a^2$$

$$\textbf{Step 2 : Put the values in expression,}$$

$$ab-a^2=2\times3-(2)^2=6-4=2$$

$$\textbf{Hence, the required value of }\mathbf{ab-a^2}\textbf{ for }\mathbf{a=2,b=3}\textbf{ is }\mathbf{2}.$$

Round off each of the following numbers to the nearest hundred, thousand ten thousand and lakh.
$$534573$$

$$\rightarrow$$ Given number : $$534573$$

Rounding off to nearest hundred : $$5,34,600$$

Rounding off to nearest thousand : $$5,35,000$$

Rounding off to nearest ten thousand : $$5,30,000$$

Rounding off to nearest lakh : $$5,00,000$$

If $$\dfrac{{\sqrt 2 + \sqrt 3 }}{{3\sqrt 2 - 2\sqrt 3 }} = a + b\sqrt 6 $$ find the value of a&b.

If $$ \dfrac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}} = a+b\sqrt{b} $$

$$ \dfrac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}} = \dfrac{(\sqrt{2}+\sqrt{3})(3\sqrt{2}+2\sqrt{3})}{(3\sqrt{2}-2\sqrt{3})(3\sqrt{2}+2\sqrt{3})} $$ (Rationalization)

$$= \dfrac{6+2\sqrt{6}+3\sqrt{6}+6}{(3\sqrt{2}^{2})-(2\sqrt{3})^{2}} $$

$$((3\sqrt{2}^{2})=9\times 2=18) $$

$$ = \dfrac{12+5\sqrt{6}}{18-12} $$ $$ (2\sqrt{3})^{2} = 4\times 3 = 12 $$

$$ = \dfrac{12+5\sqrt{6}}{6} $$

$$ = 2+\dfrac{5}{6}\sqrt{6} $$

$$\therefore a = 2 $$ and

$$ b = \dfrac{5}{6} $$

Round off each of the following numbers to the nearest hundred, thousand ten thousand and lakh.
$$473847$$

Given number : $$4,73,847$$

$$\Rightarrow$$ Rounding off to nearest hundred : $$4,73,800$$

$$\Rightarrow$$ Rounding off to nearest thousand : $$4,74,000$$

$$\Rightarrow$$ Rounding off to nearest ten thousand : $$4,70,000$$

$$\Rightarrow$$ Rounding off to nearest lakh : $$5,00,000$$

Mukesh was on diet plane. His weight $$144.55\ kg$$. He lost $$25.75\ kg$$. Find his weight after completion of his diet programme.

weight after completion$$=144.55-25.75$$

$$=118.8$$ kg

The sum of two numbers is $$6 \,78 \,90 \,781$$. If one of them is $$3 \,42 \,16 \,789$$, find the other number. Also find which of the two numbers is greater.

$$x+y=67890781$$

But, $$x=34216789$$

$$y=67890781-34216789$$

$$y=33673992$$

Clearly, $$y > x$$.

1126236_1289781_ans_149c1a33e7f74af49d260a7eb2165616.JPG

Find the value of $$5\left[ 9+1 \right] -10$$.

$$5[9+1]-10\\=5\times10-10\\=50-10\\=40$$

From the following pairs of numbers, find the reduced form of ratio of first number second number.
$$72,60$$

$$\frac{72}{60}=\frac{36}{30}\frac{12}{10}=\frac{6}{5}$$
1188301_1344233_ans_bf70a0aa98bd41ddadb4af8dfd461d9e.jpg

Find the greater and the smaller number:
$$1834,75284,111,2333,450$$

Arranging the above number is descending order

$$75284>2333>1834>450>111$$

$$\therefore$$ Greatest number $$=75284$$

and smallest number $$=111$$

Fill in the boxes with $$< , >$$, or $$=$$.
$$3\ kg\ \Box\ 300\ g$$

$$3kg, \dfrac{300}{1000}kg$$

$$[1kg =1000g]$$

$$\Rightarrow 3kg, 0.3kg$$

$$\Rightarrow 3kg > 0.3 kg$$.

1189583_1356528_ans_e639ebcfac984157b0ca1bf65ffbf44a.jpg

Find the greater and the smaller number:
$$1473,89423,100,5000,310$$

Arranging in descending order

$$89423>5000>1473>310>100$$

$$\therefore$$ Greatest number$$=89423$$

Smallest number$$=100$$

Find the greater and the smaller number in the following:
$$382,4972,18,59785,780,$$

Arranging the above numbers in descending order.

$$59785>4972>780>382>18$$

$$\therefore$$ Greater number$$=59785$$

and smaller number$$=18$$

Find the smallest and greatest numbers in each row
$$6109, 5248,9001, 2952,9019$$

Here,

The smallest number is $$2952$$.

The greatest number is $$9019$$.

$$\left\{ \dfrac { 319 }{ 100 } \times 40\times 40+8480 \right\} -\left\{ \dfrac { 314 }{ 100 } \times 30\times 30+6360 \right\} $$

$${\cfrac{319}{100}\times40\times40+8480}-{\cfrac{314}{100}\times30\times30+6360}\\=319\times4\times4+8480-314\times3\times3+6360\\=13584-9186\\=4398$$

The sum of three consecutive odd numbers is $$147$$.Find the numbers.

Three consecutive odd numbers

$$n, n + 2, n + 4$$

$$n + n + 2 + n + 4 = 147$$

$$3n + 6 = 147\Rightarrow 3n = 141$$

$$n = 47$$

$$47, 49$$ and $$51$$ are those integers.

Write the following Roman numerals in ascending order:
$$CXIX,\,XCIX,\,CXXI,\,CIX,\,CXX$$

Converting the given Roman numbers to decimal numbers:

$$CXIX=100+10+9=119$$

$$XCIX=90+9=99$$

$$CXXI=100+21=121$$

$$CIX=100+9=109$$

$$CXX=100+20=120$$

Now, arranging these numbers in ascending order:

$$99<109<119<120<121$$

$$\therefore\ XCIX<CIX<CXIX<CXX<CXXI$$ is the ascending order of the given Roman numbers.

Gopal purchased 3 meters 400 cm cloth for shirts and 1 meter 750 cm for trousers, then how much cloth he has purchased?

For shirt $$= 3\, m \,400 \,cm$$

For Trouser $$= 1 \,m \,750 \,cm$$

Total cloth purchased by Gopal $$= 3\, m \,400 \,cm$$ $$+ 1 \,m \,750 \,cm$$$$= 5 \,m \,150 \,cm$$

Divide the following.
$$4\ L\ 512\ mL\ by\ 8$$

Now, $$4$$ L $$512$$ mL $$=4,512$$ mL.

As $$1 \ L=1000 \ mL$$

When we divide $$5,412$$ mL by $$8$$ then we get,

We've,

$$\dfrac{4,512}{8}=564$$ mL.

Find the greater and the smaller number:
$$7853,7691,9999,12002,124$$

Arranging in descending order

$$12002>9999>7853>7691>124$$

$$\therefore$$ Greatest number$$=12002$$

and smallest number$$=124$$

Ramesh runs $$12\,km\,120\,m$$ every morning. How many $$m$$ does he run ?

$$1$$ $$km =1000$$ $$m.$$

Hence $$12$$ $$km =12 \times 1000$$ $$m = 12,000$$ $$m.$$

Distance he runs $$=12$$ $$km$$ $$120$$ $$m = 12$$ $$km+120$$ $$m$$

$$= 12,000$$ $$m + 120$$ $$m$$

$$ = 12,120$$ $$m $$

Ramesh runs $$12,120$$ $$m $$ every morning.

Multiply the following.
$$6\ kg\ 250\ g\ by\ 7$$

If we multiply $$6\ kg\ 250\ g\ by\ 7$$

Then we get, $$42$$ kg $$1750$$ gm

As $$1 \ kg=1000 \ gm$$

If we multiply $$6\ kg\ 250\ g\ by\ 7\Rightarrow $$ $$43$$ kg $$750$$ gm.

Solve:$$XCII-XV$$

$$XCII=90+2=92$$

$$XV=10+5=15$$

$$XCII-XV=92-15=67=LXVII$$

Divide the following.
$$3\ kL\ 408\ L\ by\ 4$$

Now,

$$3$$ kL $$408$$ L$$=3,408$$ L.

As $$1 \ kL=1000 \ kL$$

Now,

$$\dfrac{3,408}{4}=852$$ L.

Write the following in numeral form:
Seventy thousand fifty three.

$$70\times 1000+53$$

$$=70,000+53$$

$$=70,053$$

Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
$$1,08,734-47,599$$.

Given number is $$1,08,734-47,599$$
Rounding off to nearest hundreds:

$$1,80,734$$ and $$47,599$$ may be rounded off to $$1,08,700$$ and $$47,600$$ respectively.
Hence,

$$108700$$
$$-47600$$
__________
$$61100$$
__________

Rounding off to nearest tens:

$$1,08,734$$ and $$47,599$$ may be rounded off to $$1,08,730$$ and $$47,600$$ respectively.
Hence,

$$108730$$
$$-47600$$
__________
$$61130$$
__________

Write the following in numeral form:
Thirty lakh eleven thousand one.

$$30\times 1,00,000+11\times 1000+1=30,11,001$$

Hence the given number in the numeral form can be written as $$30,11,001.$$

A shopkeeper had 35 m 50 cm cloth of one kind and 24 m 25 cm cloth of another kind. How much cloth did he have altogether?

1317494_1488826_ans_21f0aa2ddaeb44da955b2e0d09f3adbf.JPG

Write the following in numeral form:
Eight thousand twelve.

$$8\times 1000+12$$

$$=8000+12$$

$$=8012$$

Write the following in numeral form:
Five lakh seven thousand four hundred six.

$$5\times 1,00,000+7\times 1000+4\times 100+6=5,07,406$$

Hence, the given number in the numeral form can be written as, $$5,07,406.$$

Write the following in numeral form:
Eight crore four lakh twenty five.

$$8\times 1,00,00,000+4\times 1,00,000+25$$

$$=8,04,00,025$$

How many thousands make a crore?

Representation of $$1$$ crore in figure is given by $$: 10000000$$

Number of zeros in $$1$$ crore $$= 7$$

Now, representation of thousand in figure is given by $$: 1000$$

Number of zeros in thousand $$= 3$$

So, Now we need to find how many thousands make a crore.

For this we need to divide one crore in figures by one thousand in figure or in a easy way we can subtract the number of zeros in a crore and number of zeros in a thousand

$$\rightarrow$$ $$7 - 3 = 4$$

Hence, number of thousand which make a crore $$= 10000$$ thousand

$$\therefore$$ $$10,000$$ thousands make $$1$$ crore.

Find the largest six-digit number which is exactly divisible by 127.

1300313_1609062_ans_bcca665ddded42b095c06c7ffcc93a20.jpg

Write the following in numeral form:
Six lakh two thousand nine.

$$6\times 1,00,000+2\times 1000+9$$

$$=6,02,009$$

Write the following number in words in the Indian system of numeration:
$$25,05,05,500$$.

1671000_1657887_ans_0b069979d0af47e291196f1119956049.png

Write the following number in words in the Indian system of numeration:
$$4,05,045$$.

1573112_1657884_ans_6aaa3f867fbc47c2878747766372096e.jpg

Write the following number in words in the Indian system of numeration:
$$42,007$$.

1573110_1657883_ans_f550c43a02da4faf906cd1eeb4969ada.jpg

Insert commas in the correct positions to separate periods and write the following number in words:
$$24798$$.

After inserting commas, the number will be 24,798.

24,798 = Twenty four thousand seven hundred ninety eight

Write the following in numeral form:
Seventeen crore sixty lakh thirty thousand fifty seven.

$$17\times 1,00,00,000+60\times 1,00,000+30\times 1000+57$$

$$=17,60,30,057$$

Write the following number in words in the Indian system of numeration:
$$7,06,04,014$$.

1573117_1657886_ans_3dab42c3178540989fb9b83fbc42e838.jpg

Write the following number in words in the Indian system of numeration:
$$35,42,012$$.

1573115_1657885_ans_64180441378d4a28a4f4e84690d11462.jpg

Write the following number in words in the Indian system of numeration:
$$5,50,50,050$$.

5,50,50,050 = Five crores fifty lakhs fifty thousand fifty

Insert commas in the correct positions to separate periods and write the following number in words:
$$857367$$.

After inserting commas, the number will be 8,57,367.

8,57,367 = Eight lakhs fifty seven thousand three hundred sixty seven

Insert commas in the correct positions to separate periods and write the following number in words.
$$4375$$.

After inserting commas, the number will be 4,375.

4,375 = Four thousand three hundred seventy five

Write all possible $$3$$-digit numbers using the digits $$6, 0, 4$$, when repetition of digits is allowed.

$$400, 406, 460, 466, 444, 404, 440, 446, 464, 600, 604, 640, 644, 646, 664, 606, 660, 666$$.

Insert commas in the correct positions to separate periods and write the following number in words.
$$10105607$$.

After inserting commas, the number will be 1,01,05,607.

1,01,05,607 = One crore one lakh five thousand six hundred seven

Insert commas in the correct positions to separate periods and write the following number in words:
$$10000007$$.

After inserting commas, the number will be 1,00,00,007.

1,00,00,007 = One crore seven

How many different $$3$$-digit numbers can be formed by using the digits $$0, 2, 5$$ without repeating any digit in the number?

Only $$4$$ numbers are possible which are $$205,250,520,502$$

We cannot use $$025$$ and $$052$$ as it is not a $$3$$ digit no.

Fill in the blank.
$$1$$ lakh$$=$$ ____ ten thousand.

$$1$$ lakh $$=1,00,000$$

$$=10,000\times 10$$

$$=10\times $$ Ten thousand

Write all possible $$3$$-digit numbers using the digit $$6, 0, 4$$, when repetition of digits is not allowed.

$$640, 460, 604, 406$$.

Insert commas in the correct positions to separate periods and write the following number in words.
$$9050784$$.

After inserting commas, the number will be 90,50,784.

90,50,784 = Ninety lakhs fifty thousand seven hundred eighty four

Fill in the blank.
$$1$$ crore $$=$$ _______lakh.

$$1$$ crore $$=1,00,00,000$$

$$=1,00,000\times 100$$

$$=100 \ \mathrm{Lakh}$$

Fill in the blank.
$$1$$ lakh$$=$$______ thousand.

$$1$$ lakh $$=1,00,000$$

$$=1000\times 100$$

$$=100\times$$ Thousand

Insert commas in the correct positions to separate periods and write the following number in words:
$$910107104$$.

1501475_1657898_ans_ab3a7918e8674e35bcb2f38232529599.jpg

Write the following numbers in digits by using international place value chart. Also, write them in expanded form.
Seven million three hundred three thousand two hundred six.

$$7,303,206$$
$$7303206=7\times 1000000+3\times 100000+0\times 10000+3\times 1000+2\times 100+0\times 10+6\times 1$$.

Rewrite the following numerals with proper commas in the international system of numeration. Also, write the number name in the international system of numeration.
$$513625$$.

International : 513,625513,625

International : Five hundred thirteen thousand six hundred twenty five.

Write the following numbers in digits by using international place value chart. Also, write them in expanded form.
Six billion one hundred ten million three thousand seven.

$$6,110,003,007$$
$$6110003007$$$$=6\times 1000000000+1\times 100000000+1\times 10000000+0\times 1000000+0\times 100000$$

$$+0\times 10000+3\times 1000+0\times 100+0\times 10+7\times 1$$.

Fill in the blank.
$$1$$ crore$$=$$_____thousand.

1 crore = 1,00,00,000

On removing commas,

1 crore = 10000000

So, 1 crore = 10000 × (1000)

1 crore= 10,000 thousand

Rewrite the following numerals with proper commas in the international system of numeration. Also, write the number name in the international system of numeration.
$$65954923$$.

Given numeral can be written as $$65,954,923$$ and the number name would be,

$$\text{Sixty five million nine hundred fifty four thousand nine hundred twenty three}$$

Rewrite the following numerals with proper commas in the international system of numeration. Also, write the number name in the international system of numeration.
$$4035672$$.

1503000_1658402_ans_72f83008c3934160995d882a3a82bf47.jpg

Write the following numbers in digits by using international place value chart. Also, write them in expanded form.
Fifty five million twenty nine thousand seven.

$$55,029,007$$
$$55029007=5\times 10000000+5\times 1000000+0\times 100000+2\times 10000+9\times 1000+0\times 100+0\times 10+7\times 1$$.

Fill in the blank.
$$1$$ crore$$=$$_____ ten thousand.

$$1$$ crore $$= 1,00,00,000$$

So, $$1$$ crore $$= 1000 × (10,000)$$

$$1$$ crore $$= 1000$$ ten thousand

Rewrite the following numerals with proper commas in the international system of numeration. Also, write the number name in the international system of numeration.
$$70902005$$.

The given number can be rewritten as $$70,902,005$$ and in words it can be written as "Seventy million nine hundred two thousand five".

Write the following number in the Indian system of numeration:
Six million five hundred forty three thousand two hundred ten.

According to the Indian system of numeration, the number will be 65,43,210 that is sixty five lakhs forty three thousand two hundred ten

Write the following numbers in the Indian system of numeration:
Three hundred twenty five million four hundred seventy nine thousand eight hundred thirty eight.

According to Indian system of numeration, the number will be 32,54,79,838 that is thirty two crores fifty four lakhs seventy nine thousand eight hundred thirty eight

Write $$10075302$$ in words and rearrange the digits to get the smallest and the largest numbers.

1,00,75,302= One crore seventy five thousand three hundred two

Rearranging the digits,

Largest number = 7,53,21,000

Smallest number = 1,00,02,357

How many lakhs make a billion?

1 billion =1,000,000,000

1 lakh=1,00,000

So, 1 billion = 10,000×(1,00,000)

1 billion =10,000 lakhs

How many lakhs make a million?

$$1.000.000=10 \times 1,00,000=10 \ lakhs$$

Round off the following number to nearest tens.
$$84$$.

1503135_1658543_ans_0331151788a64a81b4100aabac8ef12f.jpg

How many thousands make a million?

1503050_1658411_ans_24351cfb78dc4d508856ac53d8e4e410.jpg

Round off the following number to nearest tens.
$$984$$.

$$984$$ is nearer to $$980$$ than $$990$$.
So, answer is $$980$$

Write the following number in the Indian system of numeration:
Seventy six million eight five thousand nine hundred eighty seven.

In International system, the number will be expressed as 76,085,987

So, in Indian system, it will be expressed as 7,60,85,987

Round off the following number to nearest tens.
$$808$$.

$$808$$ is nearer to $$810$$ than $$800$$.
So, answer is $$810$$

Round off the following number to nearest tens.
$$98$$.

The nearest tens to 98 are 90 nd 100.

The difference between 98 and 90 is 8; while the difference between 100 and 90 is 10.

So, answer is 100.

Round off the following number to the nearest thousand.
$$9,600$$.

The nearest thousands to 9,600 are 9,000 nd 10,000.

The difference between 9,600 and 9,000 is 600; while the difference between 10,000 and 9,600 is 400.

So, answer is 10,000.

Round off the following number to the nearest thousand.
$$2,401$$.

$$2401$$ is nearer to $$2000$$ than $$3000$$

So Ans is $$2000$$

Round off the following number to nearest tens.
$$28,925$$.

$$28925$$ is at the same distance from $$28920$$ and $$28930$$.

Since the last digit is $$5$$ therefore, the given number would be rounded off to $$28930$$.

Round off the following number to nearest hundreds.
$$43,68,973$$.

$$43,68,973$$ nearer to $$43,69,000$$ than $$43,68,000$$.

So Ans is $$43,69,000$$

Round off the following number to nearest hundreds.
$$28,826$$.

1503147_1658561_ans_ee4d0520fd154f17bbb8af03efcc2ab1.jpg

Round off the following number to nearest hundreds.
$$7,42,898$$.

$$7,42,898$$ is nearer to $$7,42,900$$ than $$7,42,800$$.

So Round off is $$7,42,900$$

Round off the following number to nearest tens.
$$998$$.

1503139_1658547_ans_ca5268e8ccea4e3f940183a6e8702ae9.jpg

Round off the following number to nearest hundreds.
$$3,985$$.

$$3985$$ nearer to $$4000$$ than $$3900$$

So $$4000$$ is round off.

Round off the following number to nearest tens.
$$10,908$$.

$$10908$$ is nearer to $$10,910$$ than $$10,900$$

So Ans is $$10,910$$

Round off the following number to nearest tens.
$$12,096$$.

$$12,096$$ is nearer to $$12,100$$ than $$12,090$$
So, answer is $$12,100$$

Round off the following number to the nearest thousand:
$$436952$$

$$436952$$ is in between two thousands, which are $$436000$$ and $$437000$$.

$$436952$$ is nearer to $$437000$$ than $$436000.$$

Hence, the required answer is $$437000.$$

Round off the following number to the nearest hundred:
$$666$$

The given number $$666$$ is in between two hundreds which are $$600$$ and $$700$$ .

Difference between $$666$$ and $$600$$ is $$(666-600)=66$$

Difference between $$666$$ and $$700$$ is $$(700-666)=34$$

So, $$666$$ is nearer to $$700$$ than $$600$$

Hence, the required answer is $$700$$ .

Round off the following number to the nearest thousand.
$$9,567$$.

$$9,567$$ is nearer to $$10,000$$ than $$9,000$$
So, answer is $$10,000$$

Round off the following number to the nearest thousand.
$$26,019$$.

26019 is nearer to 26000 than 27000.

So, answer is 26000.

Round off the following to the nearest tens, hundreds and thousands.
$$45,634$$.

$$45,634$$

Rounding off to nearest tens, we get $$45,634$$ as $$45,630.$$

Rounding off to nearest hundreds, we get $$45,634$$ as $$45,600.$$

Rounding off to nearest thousands, we get $$45,634$$ as $$46,000.$$

Round off the following to the nearest tens, hundreds and thousands.
$$79,085$$.

The given number is $$79,085$$

Rounding off to nearest tens:

We see that the ones digit in $$79,085$$ is $$5$$.

Hence, the number will be rounded off to the nearest tens as $$79,090$$.

Rounding off to nearest hundreds:

We see that the tens and ones digits make $$85$$, which is more than $$50$$.

Hence, the number will be rounded off to the nearest hundreds as $$79,100$$.

Rounding off to nearest thousands:

We see that the hundreds, tens and ones digits make $$085$$, which is less than $$500$.

Hence, the number will be rounded off to the nearest thousands as $$79,000$$.

Round off the following to the nearest tens, hundreds and thousands.
$$964$$.

$$1.$$ The tens place of number 964 is 6, here we need to round off the tens place of number to make $$64$$ to $$60$$. Thus the number rounded off to nearest tens will be $$960$$.

$$2.$$ The hundreds place of number $$964$$ is $$9$$, here we need to round off the hundreds place of number $$9$$ to $$10$$ to make the required number to nearest hundreds as $$1000$$

$$3.$$ Nearest thousands of number $$964$$ is $$1000$$. As $$964$$ is much nearer to $$1000$$ than $$900$$.

Round off $$1,049$$ to the nearest tens, hundreds and thousands.

Rounding off to nearest tens:

$$1049$$ is in between $$1040$$ and $$1050$$ but it is closer to $$1050$$,

So, on rounding off to nearest tens, we get $$1050$$

Rounding off to nearest hundreds:

$$1049$$ is in between $$1000$$ and $$1100$$ but it is closer to $$1000$$

So, on rounding off to nearest hundreds, we get $$1000$$

Rounding off to nearest thousands:

$$1049$$ is in between $$1000$$ and $$2000$$ but it is closer to $$1000$$

So, on rounding off to nearest thousands, we get $$1000$$

Round off the following number to the nearest thousand.
$$7,832$$.

7832 is nearer to 8000 than 7000.

So, answer is 8000.

Round off the following number to the nearest thousand.
$$4,278$$.

At the hundred place digit is $$2$$ which is less than $$5$$

$$\therefore 4278$$ is Round off to the nearer thousand is $$4000.$$

So, answer is $$4000.$$

Round off the following measures to the nearest hundred.
$$550$$cm.

1503360_1658590_ans_7bc6af87c4f94a2cbdb39d6527cb6351.jpg

Round off the following measures to the nearest hundred.
$$360$$ gm.

1503362_1658592_ans_3c75c4fc1399429daf3f6e915e5150b0.jpg

Round off the following measures to the nearest hundred.
$$273\ l$$

$$273\ l$$ is nearer to $$300$$ than $$200$$

So Ans is $$300\ l$$

Round off the following measure to the nearest hundred.
$$Rs.\ 851$$.

$$851$$ is nearer to $$900$$ than $$800.$$ So, $$Rs.\ 851$$ is rounded off to $$Rs.\ 900$$ as the nearest hundred,

Round off the following measures to the nearest hundred.
$$2,486$$m.

2,486m

2,486 is in between 2,400 and 2,500

But since it is more closer to 2,500 than 2,400

So, when rounding off to nearest hundreds, we get 2,500

Round off the following measures to the nearest hundred.
$$417$$m.

$$417$$ is nearer to $$400$$ than $$500$$ So Ans is $$400$$

Round off the following measures to the nearest hundred.
$$940$$ kg.

$$940$$ kg is nearer to $$900$$ than $$1000$$
So answer is $$900$$ kg

Round off the following measures to the nearest hundred.
$$1,265$$ km.

$$1265$$ is nearer to $$1300$$ than $$1200$$

So Ans is $$1300$$

Round off the following measures to the nearest hundred.
Rs. $$9,080$$.

$$9,080$$ is nearer to $$9100$$ than $$9000$$

So Ans is $$9100$$

Round off the following measures to the nearest hundred.
$$820$$ mg.

$$820$$ mg is nearer to $$800$$ than $$900$$.
So, answer is $$800$$

Estimate the following by rounding off the number to its greatest place.
$$439+334+4,317$$.

1504205_1658607_ans_0bd553e9e5e64655904492152f61c61b.jpg

Estimate the following by rounding off the factor to nearest thousands.
$$12,904+2,888$$.

1503380_1658604_ans_4a5a9cae5aa343bc84dd16ed435cc315.jpg

Estimate the following by rounding off the factor to nearest thousands.
$$28,292-21,496$$.

28,292 - 21,496

On rounding off 28,292 to nearest thousands, we get 28,000

Om rounding off 21,496 to nearest thousands, we get 21,000

So, estimated difference = 28,000-21,000 =7,000

Estimate the following by rounding off the factor to nearest hundreds.
$$796-314$$.

$$796$$

$$- \underline{314}$$

$$482$$

$$482$$ is nearer to $$500$$ than $$400$$

So Answer is $$500$$

Estimate the following by rounding off the number to its greatest place.
$$898\times 785$$.

1573134_1658613_ans_b6547683f15d488f8748bb281935173f.jpg

Replace * in each of the following by < or > so that the statement is true:
(i) 2 * 5
(ii) 0 * 3
(iii) 0* -7
(iv) -18 15
(v) -235 -532
(vi) -20 * 20

(i) $$2 < 5$$
(ii) $$0 < 3$$
(iii) $$0 > -7 $$
(iv) $$-18 < 15 $$
(v) $$-235 > -532 $$
(vi) $$-20 < 20$$

List all numbers which are rounded off to nearest ten as $$370$$.

365,366,367,368,369,370,371,372,373,374 gives 370 when rounded off to nearest tens.365,366,367,368,369,370,371,372,373,37

Estimate $$875-384$$ by rounding off the factor to the nearest hundreds.

$$875$$

$$-\ 384$$

--------------

$$491$$

$$\Rightarrow 491$$ is nearer to $$500$$ than $$400$$

Hence, when $$875-384$$ rounded off to nearest hundred is $$500$$

Estimate the following by rounding off the factor to nearest hundreds.
$$730+998$$.

$$730$$

$$+\underline{\,\,998}$$

$$1728$$

$$1728$$ is nearer to $$1700 $$ than $$1800$$

So Ans is $$1700$$

Estimate the following by rounding off the number to its greatest place.
$$8,325-491$$.

8325-491

On rounding off 8325 to nearest thousands, we get 8000

On rounding off 491 to nearest hundreds, we get 500

So, estimated answer= 8000-500 =7500

Write the following in Roman numerals.
$$248$$.

1504312_1658754_ans_29f79aa91d6943b2b4cee404b948dec1.jpg

Write the following in Roman numerals.
$$4201$$.

1504327_1658760_ans_df2c64d88c5f4df6a83db1df344326aa.jpg

Write the following in Roman numerals.
$$3906$$.

1504323_1658758_ans_2a5ce1b391104ee8b82d7d172c32a6ab.jpg

Write the following in Roman numerals.
$$2718$$.

1504320_1658757_ans_d2b81c82db89404b91e67513a1efcddc.jpg

Write the following in Roman numerals.
$$10009$$.

1504328_1658761_ans_c085f94aa82d4a4f905e0cce7cb2d215.jpg

Write the following in Roman numerals.
$$44000$$.

1504329_1658762_ans_211dcaca20494f508fcec67cd7093e8b.jpg

Write the following in Roman numerals.
$$173$$.

1501989_1658753_ans_a7e019bdb4794ad59202ff8138325a34.PNG

Write the roman-numerals for the following.
$$33$$.

$$33=(10+10+10)+(1+1+1)$$

$$\times=10$$ and $$I=1$$

So, the Roman numeral will be

$$33=XXXIII$$

Write the roman-numerals for the following.
$$95$$.

1504310_1658751_ans_9cabc41d001549b7b478569379d4985e.jpg

Write the following in Roman numerals.
$$3794$$.

1504325_1658759_ans_7fa35779b3634aabaa02fbebc6207b55.jpg

Write the following in Roman numerals.
$$25819$$.

1504330_1658763_ans_03c09490e2104bc4a0468395051a8f9c.jpg

Write the largest number of $$6$$ digits and the smallest number of $$7$$ digits. Which one of these two is larger and by how much?

The largest $$6$$ digit number $$=9,99,999$$

The smallest $$7$$ digit number $$=10,00,000$$

Clearly, $$10,00,000$$ is the larger than $$9,99,999$$

And their difference$$=10,00,000-9,99,999=1$$

Hence $$10,00,000$$ is the larger than $$9,99,999$$ by $$1$$.

Fill in the blank with the appropriate symbol $$<$$ or $$>$$.
$$2300014$$______$$2300041$$.

Rules to compare the numbers:

1.The greater the number of digits, the greater is the number. (unless there are only zeros to the left of the number e.g. 007)

2.If two numbers have the same number of digits, the number with the bigger digit on the left hand side is greater.

3.If the leftmost digits are the same we compare the next digit to the right and keep doing this until the digits are different.

$$\therefore 2300014<2300041.$$

Fill in the blank with the appropriate symbol $$<$$ or $$>$$.
$$10001$$____$$100001$$.

The more the number of digits, the greater is the number.

$$10001$$$$<100001$$

Fill in the blank with the appropriate symbol $$<$$ or $$>$$.
$$25$$______$$205$$.

$$25$$ is two digit number and $$205$$ is three digit number.

So, clearly $$25<205$$

Write the following numerals in Indian system of numeration.
$$27943$$.

Given : 27,943

Indian- Twenty seven thousand nine hundred and forty three.

Write the following numerals in Indian system of numeration.
$$823514$$.

Indian- 8,23,514

Indian- Eight lakh twenty three thousand five hundred fourteen.

Fill in the blank.
$$1$$ crore$$=$$________ million.

1507685_1660215_ans_185b916be94f46aa8d888af4963513b0.jpg

Write the following numerals in Indian system of numeration.
$$53428769$$.

Indian-5,34,28,769

Indian-Five crore thirty four lakh twenty eight thousand seven hundred sixty nine only.

Fill in the blank.
The smallest four digit number with four different digits is ________.

Smallest 4 digit number with four different digits will be 1023

So, the answer is 1023

Estimate the sum $$(42505+27807+21397)$$ to the nearest thousand.

$$42505$$ estimated to the nearest thousand $$= 43000$$

$$27807$$ estimated to the nearest thousand $$= 28000$$

$$21397$$ estimated to the nearest thousand $$= 21000$$

Now, the sum of the estimated numbers is $$43000+28000+21000=92000$$

Hence, the sum is $$92000$$.

Write the following numerals in Indian system of numeration.
$$7421932$$.

Indian- 74,21,932

Indian-Seventy four lakh twenty one thousand nine hundred thirty two.

Fill in the blank.
$$1$$ billion $$=$$________ crore.

1507681_1660211_ans_6c0f4c12e0cd4af986f4355b399f5eda.jpg

Estimate the product $$475\times 225$$ rounding off each number to the nearest hundred.

In $$475$$ the last two digits i.e., $$75$$ is greater than $$50$$.

Therefore, $$1$$ will be added to the 3rd last digit and the last two digits will become zero.

After rounding to nearest hundred we will get $$500$$.

In $$225$$ the last two digit i.e., $$25$$ is less than $$50$$

Thus, the 3rd last will remain same and the last digit will become zero.

After rounding to nearest ten we will get $$200$$.

Hence, the required product is $$500\times 200 = 1,00,000$$

Write the numeral for the following numbers:
Nine thousand eighteen

The numeral form of nine thousand eighteen is: 9018

Write the numeral for the following numbers:
Fifty- four thousand seventy-three

The numeral form of fifty four thousand seventy-three is 54073

Write the numeral for each of the following numbers:
Six crore five lakh fifty-seven

Six crore $$=60000000$$

Five lakh $$=500000$$

Fifty seven $$=57$$

Let $$N$$ be the required number.

$$N=60000000+500000+57$$

$$=60500057$$

Thus the numeral form of six crore five lakh fifty-seven is: $$60500057$$

Write the following numbers in expanded form:
$$5,36,18,493$$

The given number is $$5,36,18,493$$
The expanded form of $$5,36,18,493 = (5 \times 10000000) + (3 \times 1000000) + (6 \times 100000) + (1 \times 10000) + (8 \times 1000) + (4 \times 100) +\\ (9 \times 10) + (3 \times 1)$$

Write the following numbers in expanded form:
$$24,05,609$$

The given number is $$24,05,609$$
The expanded form of $$24,05,609 = (2 \times 1000000) + (4 \times 100000) + (5 \times 1000) + (6 \times 100) + (9 \times 1)$$

Write the numeral for the following numbers:
Fifteen crore fifty lakh twenty thousand sixty-eight

The numeral form of fifteen crore fifty lakh twenty thousand sixty-eight is: $$155020068$$

Write the numeral form for the following numbers:
Three lakh two thousand five hundred six

The numeral form of three lakh two thousand five hundred six is: $$302506$$

Write the following numbers in expanded form:
$$3,08,927$$

The given number is $$3,08,927$$
The expanded form of $$3,08,927 = (3 \times 100000) + (8 \times 1000) + (9 \times 100) + (2 \times 10) + (7 \times 1)$$

Write the following numbers in expanded form:
$$9,10,10,510$$

The given number is $$9,10,10,510$$
The expanded for of $$9,10,10,510 = (9,10,10,510 = (9 \times 10000000) + (1 \times 1000000) + (1 \times 10000) + (5 \times 100) + (1 \times 10)$$

Write the following numbers in expanded form:
$$15,768$$

The given number is $$15,768$$
The expanded form of $$15,768 = (1 \times 10000) + (5 \times 1000) + (7 \times 100) + (6 \times 10) + ( 8 \times 1)$$

Write the numeral for the following number:
Twenty lakh ten thousand eight

The numeral form of twenty lakh ten thousand eight is: $$2010008$$

Write the corresponding numeral for the following:
$$6 \times 10000 + 2 \times 1000 + 5 \times 100 + 8 \times 10 + 4 \times 1$$

The given expanded form is $$6 \times 10000 + 2 \times 1000 + 5 \times 100 + 8 \times 10 + 4 \times 1$$
The numeral number is $$62584$$

Write the corresponding numeral for the following:
$$3 \times 1000000 + 4 \times 100000 + 6 \times 1000 + 5 \times 100 + 7 \times 1$$

The given expanded form is $$3 \times 1000000 + 4 \times 100000 + 6 \times 1000 + 5 \times 100 + 7 \times 1$$
The numeral number is $$3406507$$

Round the following number to the nearest ten:
$$16378$$

$$16378$$
Here $$8$$ is in once digits place
$$8 > 5$$
$$\therefore$$ required rounded number is $$16380$$

Round the following number to the nearest ten:
$$3869$$

$$3869$$
Here $$9$$ is in once place
$$9 > 5$$
$$\therefore$$ required rounded number is $$3870$$

Round the following number to the nearest hundred:
$$814$$

$$814$$
Here tens digits place is $$1$$
$$1 < 5$$
$$\therefore$$ rounded number is $$810$$

Write the corresponding numeral for the following:
$$2 \times 10000000 + 5 \times 100000 + 7 \times 1000 + 9 \times 100 + 5 \times 1$$

The given expanded form is $$2 \times 10000000 + 5 \times 100000 + 7 \times 1000 + 9 \times 100 + 5 \times 1$$
The numeral number is $$20507905$$

Round the following number to the nearest hundred:
$$1254$$

$$1254$$
Here tens digits place is $$5$$
$$5 = 5$$

and hundreds digit is even
$$\therefore$$ rounded number is $$1300$$

Round the following number to the nearest ten:
$$173$$

$$173$$
Here $$3$$ is in units digits place
$$3 < 5$$

Thus, units digits should be rounded to zero.
$$\therefore$$ required rounded number is $$170$$

Write the corresponding numeral for the following:
$$5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1$$

The given expanded form is $$5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1$$
The numeral number is $$581623$$

Round the following number to the nearest ten:
$$36$$

$$36$$
Here $$6$$ is in once digits place
$$6 > 5$$
$$\therefore$$ required rounded number is $$40$$

Round the following number to the nearest ten thousand:
$$34890$$

Thousand's digit of $$34890$$ is $$4$$ that is less than $$ 5$$.
$$\therefore$$ After rounding off to the nearest ten thousand the required number is $$30000$$

Round the following number to the nearest hundred:
$$98165$$

$$98165$$
Here tens digits place is $$6$$
$$6 > 5$$
$$\therefore$$ required rounded number is $$98200$$

Round off the following number to the nearest thousand:
$$4826$$

The given number is $$4826$$.

Here $$8$$ is in hundred digits place, and $$8 > 5$$.

So, we have to add $$1$$ with the thousand digit.

Thus, the required rounded number is $$5000$$.

Round the following number to the nearest ten thousand:
$$26340$$

Thousand digits number is $$6 > 5$$
$$\therefore$$ required number is $$30000$$

Round the following number to the nearest hundred:
$$43126$$

$$43126$$
Here tens digits place is $$2$$
$$2 < 5$$

Therere, $$126$$ would be rounded to $$100$$
$$\therefore$$ Required rounded number is $$43100$$

Estimate the sum to the nearest ten:
$$(57 + 34)$$

Estimated value to the nearest ten of $$57 = 60$$
Estimated value to the nearest ten of $$34 = 30$$
Total required estimation $$= ( 60 + 30) = 90$$

Round the following number to the nearest ten thousand:
$$272685$$

Thousand digits number is $$2 < 5$$
$$\therefore$$ required number is $$270000$$

Round the following number to the nearest thousand:
$$793$$

Here $$7$$ is in hundred digits place
$$7 > 5$$
$$\therefore$$ required rounded number is $$1000$$

Round the following number to the nearest thousand:
$$16719$$

Here $$7$$ is in hundred digits place
$$7 > 5$$
$$\therefore$$ required rounded number is $$17000$$

Estimate the sum to the nearest ten:
$$(43 + 78)$$

Estimated value to the nearest ten of $$43 = 40$$
Estimated value to the nearest ten of $$78 = 80$$
Total required estimation $$= ( 40 + 80) = 120$$

Estimate the sum to the nearest ten:
$$(463 + 182)$$

Estimated value to the nearest ten of $$463 = 460$$
Estimated value to the nearest ten of $$182 = 180$$
Total required estimation $$= ( 460 + 180) = 640$$

Estimate the sum to the nearest ten:
$$(86 + 19)$$

Estimated value to the nearest ten of $$86 = 90$$
Estimated value to the nearest ten of $$19 = 20$$
Total required estimation $$= ( 90 + 20) = 110$$

Estimate the sum to the nearest hundred:
$$(236 + 689)$$

Estimated value to the nearest hundreds of $$236 = 200$$
Estimated value to the nearest hundreds of $$689 = 700$$
Total required estimation $$= (200 + 700) = 900$$

Estimate the sum to the nearest ten:
$$(14 + 69)$$

Estimated value to the nearest ten of $$14 = 10$$
Estimated value to the nearest ten of $$69 = 70$$
Total required estimation $$= ( 10 + 70) = 80$$

Estimate the sum to the nearest hundred:
$$(3280 + 4395)$$

Estimated value to the nearest hundreds of $$3280 = 3300$$
Estimated value to the nearest hundreds of $$4395 = 4400$$
Total required estimation $$= (3300 + 4400) = 7700$$

Estimate the sum to the nearest hundred:
$$(458 + 324)$$

Estimated value to the nearest hundreds of $$458 = 500$$
Estimated value to the nearest hundreds of $$324 = 300$$
Total required estimation $$= (500 + 300) = 800$$

Estimate the sum to the nearest hundred:
$$(170 + 395)$$

Estimated value to the nearest hundreds of $$170 = 200$$
Estimated value to the nearest hundreds of $$395 = 400$$
Total required estimation $$= (200 + 400)$$

$$ = 600$$

Estimate the sum to the nearest ten:
$$(356 + 275)$$

Estimated value to the nearest ten of $$356 = 360$$
Estimated value to the nearest ten of $$275 = 280$$
Total required estimation $$= ( 360 + 280) = 640$$

Estimate the sum to the nearest ten:
$$(538 + 276)$$

Estimated value to the nearest ten of $$538 = 540$$
Estimated value to the nearest ten of $$276 = 280$$
Total required estimation $$= ( 540 + 280) = 820$$

Estimate the sum to the nearest ten:
$$(77 + 63)$$

Estimated value to the nearest ten of $$77 = 80$$
Estimated value to the nearest ten of $$63 = 60$$
Total required estimation $$= ( 80 + 60) = 140$$

Estimate the difference to the nearest hundred:
$$(957 - 578)$$

Estimated value to the nearest hundreds of $$957 = 1000$$

Estimated value to the nearest hundreds of $$578 = 600$$

$$\therefore$$ required estimation $$= (1000 - 600) = 400$$

Estimate the sum to the nearest thousand:
$$(32836 + 16466)$$

Estimated value to the nearest thousands of $$32836 = 33000$$
Estimated value to the nearest thousands of $$16466 = 16000$$
Total required estimation $$= (33000 + 16000) = 49000$$

Estimate the difference to the nearest ten:
$$(53 - 18)$$

Estimated value to the nearest ten of $$53 = 50$$

Estimated value to the nearest ten of $$18 = 20$$

$$\therefore$$ required estimation $$= (50 - 20) = 30$$

Estimate the sum to the nearest thousand:
$$(46703 + 11375)$$

Estimated value to the nearest thousands of $$46703 = 47000$$
Estimated value to the nearest thousands of $$11375 = 11000$$
Total required estimation $$= (47000 + 11000) = 58000$$

Estimate the difference to the nearest hundred:
$$(678 - 215)$$

Estimated value to the nearest hundreds of $$678 = 700$$

Estimated value to the nearest hundreds of $$215 = 200$$

$$\therefore$$ required estimation $$= (700 - 200) = 500$$

Estimate the difference of $$(97 - 38)$$ to the nearest ten

Estimated value to the nearest ten of $$97 = 100$$

Estimated value to the nearest ten of $$38 = 40$$

$$\therefore$$ required estimation $$= (100 - 40) = 60$$

Estimate the sum to the nearest hundred:
$$(10083 + 29380)$$

Estimated value to the nearest hundreds of $$10083 = 10080$$
Estimated value to the nearest hundreds of $$29380 = 29400$$
Total required estimation $$= (10080 + 29400) = 39500$$

Estimate the sum to the nearest hundred:
$$(5130 + 1410)$$

Estimated value to the nearest hundreds of $$5130 = 5100$$
Estimated value to the nearest hundreds of $$1410 = 1400$$
Total required estimation $$= (5100 + 1400) = 6500$$

There are $$54$$ balls in box A and $$79$$ balls in box Estimate the total number of balls in nearest tens, if both the boxes taken together

Total number of balls in box A $$= 54$$
Total number of balls in box B $$= 79$$
Total number of estimation of balls in box $$A = 50$$
Total number of estimation of balls in box $$B = 80$$
Total number of estimation of balls in both the boxes $$= (50 + 80)$$
$$= 130$$

Estimate the difference to the nearest ten:
$$(409 - 148)$$

Estimated value to the nearest ten of $$409 = 410$$

Estimated value to the nearest ten of $$148 = 150$$

$$\therefore$$ required estimation $$= (410 - 150) = 260$$

Express the following as a Roman numeral:
$$36$$

Roman number of $$36$$ is written as $$(10 + 10 + 10 + 6) = XXXVI$$

Express the following as a Roman numeral:
$$29$$

Roman number of $$29$$ is written as $$(10 + 10 + 9) = XXIX$$

Express the following as a Roman numeral:
$$14$$

Roman number of $$14$$ is written as $$(10 + 4) = XIV$$

Estimate the difference to the nearest hundred:
$$(7258 - 2429)$$

Estimated value to the nearest hundreds of $$7258 = 7300$$

Estimated value to the nearest hundreds of $$2429 = 2400$$

$$\therefore$$ required estimation $$= (7300 - 2400) = 4900$$

Express the following as a Roman numeral:
$$8$$

Roman number of $$8$$ is written as $$(5 + 3) = VIII$$

Express the following as a Roman numeral:
$$43$$

Roman number of $$43$$ is written as $$(50 - 10) + 3 = XLIII$$

Estimate the difference to the nearest hundred:
$$(5612 - 3095)$$

Estimated value to the nearest hundreds of $$5612 = 5600$$

Estimated value to the nearest hundreds of $$3095 = 3100$$

$$\therefore$$ required estimation $$= (5600 - 3100) = 2500$$

Express the following as a Roman numeral:
$$73$$

Roman number of $$73$$ is written as $$(50 + 10 + 10 + 3) = LXXIII$$

Express the following as a Roman numeral:
$$61$$

Roman number of $$61$$ is written as $$(50 + 10 + 1) = LXI$$

Express the following as a Roman numeral:
$$54$$

Roman number of $$54$$ is written as $$(50 + 4) = LIV$$

Express the following as a Roman numeral
$$475$$

Roman numeral of $$475 = (500 - 100) + 50 + 10 + 10 + 5 = CDLXXV$$

Express the following as a Roman numeral
$$195$$

Roman numeral of $$195 = (100) + (100 - 10 ) + 5 = CXCV$$

Express the following as a Roman numeral:
$$81$$

Roman number of $$81$$ is written as $$(50 + 10 + 10 + 10 + 1) = LXXXI$$

Express the following as a Roman numeral:
$$99$$

Roman number of $$99$$ is written as $$(100 - 10) + 9 = XCIX$$

Express the following as a Roman numeral
$$341$$

Roman numeral of $$341 = 100 + 100 + 100 + (50 - 10) + 1 = CCCXLI$$

Express the following as a Roman numeral:
$$164$$

Roman numeral of $$164 = (100 + 50 + 10 + 4) = CLXIV$$

Express the following as a Roman numeral:
$$91$$

Roman number of $$91$$ is written as $$(100 - 10) + 1= XCI$$

Express the following as a Roman numeral
$$226$$

Roman numeral of $$226 = (100 + 100 + 10 + 10 + 6) = CCXXVI$$

Express the following as a Roman numeral:
$$114$$

Roman number of $$114$$ is written as $$(100 + 10) + 4 = CXIV$$

Express the following as a Roman numeral:
$$105$$

Roman number of $$105$$ is written as $$(100 + 5) = CV$$

Express the following as a Roman numeral
$$611$$

Roman numeral of $$611 = 500 + 100 + 11 = DCXI$$

Write the following number in numeral form and place commas correctly:
Nine crore five lakh forty one.

Nine crore five lakh forty one. $$=9,05,00,041$$

Fill in the blanks:
1 billion = ......... hundred million.

1 billion = ten hundred million.

If a = -8, b = -7, c = 6, verify that (a+b) + c = a+ (b+c)

From the Associative law of Addition
$$= {-8+ (-7)} +6= -8 + {(-7) +6}$$
Left hand side (LHS),
$$= {-8+ (-7)} +6$$
$$= {-8-7} +6$$
$$= {-15} + 6$$
$$= -9$$
Right hand side (RHS),
$$=-8 + {(-7) +6}$$
$$=-8 + {-7+6}$$
$$=- 8 + {-1}$$
$$=-8-1$$
$$=-9$$
By comparing LHS and RHS,
$$LHS=RHS$$

Express the following as a Roman numeral
$$596$$

Roman numeral of $$596 = 500 + (100 - 10) + 6 = DXCVI$$

Express the following as a Roman numeral
$$759$$

Roman numeral of $$759 = 500 + 100 + 100 + 59 = DCCLIX$$

If a = -9 and b = -6, show that (a-b) $$\neq$$ (b-a)

From the Commutative law of Subtraction
Left hand side (LHS),
$$= {(-9)-(-6)}$$
$$= {-9+6}$$
$$=-{9-6}$$
(Take out the –ve sign outside and do subtract smaller from bigger number)
$$=-{3}$$
$$=-3$$
Right hand side (RHS),
$$= {(-6)-(-9)}$$
$$= {-6+9}$$
$$=-{6-9}$$
(Take out the –ve sign outside and do subtract smaller from bigger number)
$$=-{-3}$$
$$=3$$
By comparing LHS and RHS
$$LHS \neq RHS$$

Insert commas suitably and write the following numbers in words in the Indian system and the International system of numeration.
$$506723$$

$$506723 $$
Indian system,
Five lakh six thousand seven hundred and twenty three. $$= 5,06,723$$
International system,
Five hundred six thousand seven hundred twenty three $$=206,723$$

Write the following number in numeral form and place commas correctly:
Fifty eight million four hundred twenty three thousand two hundred two.

Fifty eight million four hundred twenty three thousand two hundred two $$=58,423,202$$

Write the following number in numeral form and place commas correctly:
Seventy three lakh seventy thousand four hundred seven.

Seventy three lakh seventy thousand four hundred seven. $$=73,70,407$$

In the following pairs of numbers, state which number is smaller:
$$41338, 1139$$

$$1139$$ is smaller.

Use the appropriate symbol $$<$$ or $$>$$ to fill in the blanks:
$$8315 .... 8037$$

$$8315 > 8037$$

Use the appropriate symbol $$<$$ or $$>$$ to fill in the blanks:
$$173 ... 189$$

$$173$$ is less than $$189$$

$$173 < 189$$

Find the greatest and the smallest numbers in the row:
$$9853, 7691, 9999, 12002.$$

$$7691$$ is the smallest number and
$$12002$$ is the greatest number.

Find the greatest and the smallest numbers in the row:
$$71834, 75284, 571, 2333, 594$$

$$571$$ is the smallest number and
$$75284$$ is the greatest number.

Use the appropriate symbol $$<$$ or $$>$$ to fill in the blanks:
$$1058 .... 1074$$

$$1058 < 1074$$

Determine the difference of the place value of two $$7's$$ in $$37014472$$ and write it in words in international system.

The given number in International system can be written as $$37,014,472$$
The place value of 7 at ten's place $$= 7 \times 10 = 70$$
The place value of 7 at 7 million's place $$= 7 \times 1,000,000 = 7,000,000$$
The required difference $$= 7,000,000 - 70 = 6,999,930$$
Six million nine hundred ninty nine thousand nine hundred thirty.

In the following pairs of numbers, state which number is smaller:
$$25431, 24531$$

$$24531$$ number is smaller.

In the following pairs of numbers, state which number is smaller:
$$553, 503$$

$$503$$ number is smaller.

Round off the following numbers to their nearest tens:
$$77$$

The digit at the unit place is $$7$$, which is greater than $$5.$$ Hence, the rounded-off number to the nearest tens is equal to $$ 80$$.

Estimate the following number to their nearest thousands:
$$5706$$

The digit at hundreds place is $$7,$$ which is greater than $$5.$$
Hence, the rounded off number to nearest thousands $$= 6000.$$

Round off the following numbers to their nearest tens:
$$999$$

The digit at unit place is $$9,$$ which is greater than $$5.$$
Hence, the rounded off number to nearest tens $$= 1000.$$

Estimate $$53961$$ to its nearest hundred.

The digit at tens place is $$6,$$ which is greater than $$5.$$

Hence, the rounded off number to nearest hundreds $$= 54000.$$

Estimate the following number to their nearest hundreds:
$$555555$$

The digit at tens place is $$5,$$ which is equal to $$5.$$
Hence, the rounded off number to nearest hundreds $$= 555600.$$

Estimate the following number to their nearest hundreds:
$$32057$$

The digit at tenss place is $$5,$$ which is equal to $$5$$.
Hence, the rounded off number to nearest hundreds $$= 32100.$$

Round off the following numbers to their nearest tens:
$$903$$

The digit at unit place is $$3,$$ which is less than $$5.$$
Hence, the rounder off number to nearest tens $$= 900.$$

Round off the following numbers to their nearest tens:
$$70 \,1205$$

The digit at unit place is $$5$$, which is equal to $$5.$$
Hence, the rounded off number to nearest tens $$= 701210$$

Estimate the following number to their nearest thousands:
$$47,599$$

The digit at hundred place is $$5,$$ which is equal to $$5.$$
Hence, the rounded off number to nearest thousands $$= 48000.$$

Estimate the following number to their nearest thousands:
$$378$$

The digit at hundred place is $$3,$$ which is less than $$5.$$
Hence, the rounded off number to nearest thousands $$= 0.$$

Estimate the following number to their nearest hundreds:
$$1246$$

The digit at tens place is $$4,$$ which is less than $$5.$$
Hence, the rounded off number to nearest hundreds $$= 1200.$$

Fill in the blanks:
Both Indian and International systems of numeration have .............. period in common.

Both Indian and International systems of numeration have ones period in common.

Estimate the following by rounding off each number nearest to its greatest place:
$$730 + 998$$

Rounding off $$730$$ to its greatest place i.e. hundred place $$= 700$$
Rounding off $$998$$ to its greatest place i.e.
hundreds place $$= 1000$$
Hence, estimated sum $$= 700 + 1000 = 1700$$

Fill in the blanks:
The number $$5079$$ when estimated to the nearest hundreds is ................

The number $$5079$$ when estimated to the nearest hundreds is $$5100.$$

Estimate the following by rounding off each number nearest to its greatest place:
$$5,290 + 17,986$$

Rounding off $$5,290$$ to its greatest place i.e.
thousands place $$= 5000$$
Rounding off $$17,986$$ to its greatest place i.e.
thousands place $$= 18,000$$
Hence, estimated sum $$= 5,000 + 18,000 = 23,000$$

Fill in the blanks:
In the International system of numeration, commas are placed from ............ after every .......... digits.

In the International system of numeration, commas are placed from right after every $$3$$ digits

Estimate the following by rounding off each number nearest to its greatest place:
$$796 - 314$$

Rounding off $$796$$ to its greatest place i.e.
hundreds place $$= 800$$
Rounding off $$314$$ to its greatest place i.e.
hundreds place $$= 300$$
Hence, estimated difference$$ = 800 - 300 = 500$$

Estimate the following number to their nearest thousands:
$$1,09,736$$

The digit at hundreds place is $$7,$$ which is greater than $$5.$$
Hence, the rounded off number to nearest thousands $$= 1,10,000$$.

Estimate the following by rounding off each number nearest to its greatest place:
$$28,292 - 21,496$$

Rounding off $$28,292$$ to its greatest place i.e.
thousands place $$= 28,000$$
Rounding off $$21,496$$ to its greatest place i.e.
thousands place $$= 21,000$$
Hence, estimated difference difference $$= 28,000 - 21,000 = 7,000$$

Estimate $$6554 - 677$$ by estimating the numbers to their nearest greatest places

Greatest places $$(6554 - 677)$$
$$\Rightarrow 7000 - 700 = 6300$$

Estimate $$6554 - 677$$ by estimating the numbers to their nearest hundreds

$$(6554-677)$$
Nearest Hundreds $$=6600-700$$
$$\Rightarrow 6600 - 700 = 5900$$

Estimate $$6554 - 677$$ by estimating the numbers to their nearest thousands

Nearest Thousands $$=6554=7000$$
Nearest Thousands $$ = 677=1000$$
$$\Rightarrow 7000 - 1000 = 6000$$

Insert commas suitably and write the number $$30189301$$ in words in Indian and International system of numeration.

Indian system,
Three crore one lakh eighty nine thousand three hundred one $$=3,01,89, 301$$
International system,
Thirty million one hundred eighty nine thousand three hundred one $$=30, 189, 301$$

Write all $$4$$-digit numbers that can be formed with the digits $$2$$ and $$5$$, using both digits equal number of time. Also find their sum.

Thousand	Hundred	Tens	Ones
2	2	5	5
2	5	5	2
2	5	2	5
5	2	2	5
5	2	5	2
5	5	2	2

Possible numbers are: $$2255, 2552, 2525, 5225, 5252, 5522$$
and their sum $$= 2255 + 2552 + 2525 + 5225 + 5252 + 5522 = 23331$$

Write the numeral for the following numbers and insert commas correctly:
One hundred four million seven hundred twenty two thousand three hundred ninety four.

One hundred four million seven hundred twenty two thousand three hundred ninety four. $$=104,722,394$$

Write the numeral for the following numbers and insert commas correctly:
Six crore nine lakh forty seven

Six crore nine lakh forty seven $$=6,09,00,047$$

Using the digits $$ 2,4,5 $$ and $$ 3 $$ once, write the smallest four-digit number.

The required number is $$ 2345 $$ is the smallest four digit decimal number.

Of the following numbers which is the greatest and which is the smallest?
$$38051425,\ 30040700, \ 67205602$$

Arrange the numbers in descending order

$$67205602 > 38051425 > 30040700$$

$$\textbf{Hence, the largest number is 67205602}$$

$$\textbf{And the smallest number is 30040700}$$

$$10$$ million $$=_______$$ crore.

$$10$$ million $$=10,000,000=1 $$ followed by $$7$$ zeros$$=1,00,00,000=1$$ crore

Convert $$ 5201\ g $$ to $$ kg. $$

We know that,

$$ 1\ kg = 1000 \ g $$

$$\Rightarrow 1\ g = \dfrac {1}{1000}\ kg $$

$$ \Rightarrow 5201\ g = \dfrac {1}{ 1000} \times 5201\ kg $$

$$ \therefore 5201 g = \dfrac {5201}{1000} = 5.201 kg $$

The length of river 'Narmada' is about $$1290\ km$$. Its length in meters is ________.

We know that,

$$1\ km=1000\ m$$

$$\Rightarrow1290\ km=1290 \times 1000\ m=1290000\ m$$

Hence the length of 'Narmada' river in meters is $$1290000\ m.$$

Fill in the blanks to make the statements true.
Writing of numbers from the greatest to the smallest is called an arrangement in _____ order.

Writing of numbers from the greatest to the smallest is called an arrangement in $$\underline{\textbf{descending}}$$ order.

As per the census of $$2001$$, of population of four states is given below. Arrange the states in ascending and descending order or their population.
Maharashtra $$96878627$$
Andhra pradesh $$76210007$$
Bihar $$82998509$$
Uttar predesh $$166197921$$

$$\textbf{Step 1: Arranging in ascending order}$$

Ascending order - process of arranging numbers from smallest to biggest.

$$76210007 < 82998509 < 96878627 < 166197921$$

$$\therefore$$ Ascending order is $$76210007, 82998509, 96878627, 166197921$$

$$\textbf{Hence, the arrangement of the states in ascending order of their population:}$$

$$\textbf{Andhra Pradesh, Bihar, Maharashtra and Uttar Pradesh}$$

$$\textbf{Step 2: Arranging in descending order:}$$

Now for descending order just reverse the above order, which is

$$\textbf{Uttar Pradesh, Maharashtra, Bihar and Andhra Pradesh}$$

The distance between Sringar and Leh is $$422$$ $$km$$. The same distance in meter is ______.

We know that,

$$1\ km=1000 \ m$$

$$\therefore 422\ km=422 \times 1000\ m$$

$$\Rightarrow422\ km=422000\ m$$

In Roman Numeration, the symbol $$X$$ can be subtracted from ______, $$M$$ and $$C$$ only.

In Roman Numeration,

$$X$$ stands for $$10$$

$$L$$ stands for $$50$$

$$C$$ stands for $$100$$

$$M$$ stands for $$1000$$

So, in Roman Numeration, the symbol $$X$$ can be subtracted from $$\boxed{L}$$, $$M$$ and $$C$$ only.

Fill in the blanks to make the statements true.
The number five Crore twenty three lakh seventy eight thousand four hundred one can be written, using commas, in the Indian System of numeration as ______.

Crores	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Units
$$5$$	$$2$$	$$3$$	$$7$$	$$8$$	$$4$$	$$0$$	$$1$$

The number is $$52378401$$

In the Indian system of numeration the first comma is placed after three digits from right and the following commas after every two digits.

So the number written using commas is $$5,23,78,401$$

$$\therefore$$ $$\textbf{The given number in Indian system of numeration using commas is 5, 23, 78, 401}$$.

The population of Pune was $$2,538,473$$ in $$2001$$. Round off to nearest thousands, the population was ______.

We have to round off to nearest thousand,

$$\therefore$$ thousandth place =$$8$$

places before that =$$473$$

Now, $$473<500$$

So, we will add $$0$$ to thousandth place and write zeros in place of above three digits.

$$\therefore$$ Round off is $$2,538,000$$

The population of Pune was $$2,538,473$$ in $$2001$$. Round off to nearest thousands, the population was $$\boxed{2,538,000}$$.

In a city, polio drops were given to $$2,12,583$$ children on Sunday in March $$2008$$ and to $$2,16,813$$ children in the next month. Find the difference of the number of children getting polio drops in the two months.

$$\textbf{Difference of number of childrens in the two months}$$

= Number of children in April - Number of children in march

= $$2,16,813 - 2,12,583$$

= $$4, 230$$

$$\textbf{Hence, the difference of the number of children getting polio drops in the two months is 4,230}$$

Find the difference between the largest number of seven digits and the smallest number of eight digits.

Largest number of $$7$$ digits $$= 9999999$$

Smallest number of $$8$$ digits $$= 10000000$$

Difference $$= 10000000 − 9999999$$

$$= 1$$

$$\textbf{Hence, the difference between the largest number of seven digits and the smallest number of eight digits is 1}$$.

The number $$66$$ in Roman numerals is ______.

$$66=50+10+5+1$$

In Roman Numeration,

$$I$$ stands for $$1$$

$$V$$ stands for $$5$$

$$X$$ stands for $$10$$

$$L$$ stands for $$50$$

$$66=50+10+5+1=LXVI$$

The smallest $$6$$ digit natural number ending in $$5$$ is _____ .

So, unit place must be $$5$$

To make smallest number we can use all $$0$$ but can't use $$0$$ at $$1^{st}$$ place, otherwise it will become $$1$$ digit number.

Now, $$1^{st}$$ place must be $$1$$ and other digits are $$0$$

$$\therefore$$ The smallest $$6$$ digit natural number ending in $$5$$ is $$100005$$

Make the greatest and the smallest $$5$$ digits numbers using different digit in which $$5$$ appears at ten's place.

$$\textbf{Making the greatest and the smallest 5-digit numbers using different digits}$$

Digits are $$0, 1, 2, 3, 4, 5, 6, 7, 8, 9$$

$$5$$ always appear at ten's place = _ _ _ $$5$$ _

For greatest number place $$9$$ at the highest place value and then $$8$$ and $$7$$ and in units place $$6$$.

$$\textbf{Therefore the greatest number is 98756}$$

Now for smallest number take the digit $$1$$, as a number cannot start with $$0$$

Then write $$0$$ and $$2$$ in the next places and $$3$$ in units place.

$$\textbf{Therefore the smallest number is 10253}$$

$$\textbf{Hence, the greatest and least 5-digit numbers are 98756 and 10253 respectively}$$.

A box contains $$50$$ packets of biscuits each weighing $$120\ g$$. How many such boxes can be loaded in a van which cannot carry beyound $$900\ kg$$?

$$\textbf{Step 1: Finding the weight of one box:}$$

Weight of $$1$$ box = Number of packets weight of one packet

= $$50 \times 120\ g$$

= $$6000\ g$$

= $$6\ kg$$ (since $$1\ kg = 1000\ g$$)

Therefore weight of A box = $$6\ kg$$

$$\textbf{Step 2: Finding number of boxes the van can carry}$$

Number of boxes van can carry $$= \dfrac{\text{Total weight the van carry}}{\text{weight of one box}}$$

$$= \dfrac{900}{6}$$

$$= 150$$

$$\textbf{Hence, the number of boxes the van can carry is 150}$$.

A mobile number consists of ten digit. The first four digits of the number are $$9,9,8$$ and $$7$$. The last three digits are $$3,5$$ and $$5$$. The remaining digits are distinct and make the mobile number, the greatest possible number. What are these digits?

$$\textbf{Making the phone number:}$$

First four fixed digits are $$9987$$

And last three fixed digits are $$355$$

Remaining numbers are $$6, 4, 2$$ and $$0$$

For the greatest possible phone number, we need to consider the greatest of the digits, all three distinct and

arrange them in descending

$$\underline{6}\ \underline{4}\ \underline{2}$$

Therefore, possible largest number is $$\underline{9}\ \underline{9}\ \underline{8}\ \underline{7}\ \underline{6}\ \underline{4}\ \underline{2}\ \underline{3}\ \underline{5}\ \underline{5}$$

$$\textbf{Hence, the greatest possible phone number is 9987642355}$$

In a five-digit number, digit at ten's place is $$4$$ digit at unit's place is one fourth of ten's place digit, digit at hundred's place is $$0$$ digit at thousand's place is $$5$$ times of the digit at unit's place and ten thousand's place digit is double the digit at ten's place. Write the number.

$$\textbf{Formation of the five digit number}$$

Digit at ten's place $$= 4$$

Digit at units place $$= \dfrac{1}{4}\ th$$ of ten's place

$$= \dfrac{1}{4} \times 4$$

$$= 1$$

Digit at hundreds place $$= 0$$

Digit at thousand's place $$= 5 \times $$ units place

$$= 5 \times 1$$

$$= 5$$

Digit at ten's thousand's place $$= 2 \times$$ digit at ten's place

$$= 2 \times 4$$

$$= 8$$

$$\therefore$$ The five digit number formed $$= 85041$$

$$\textbf{Hence, the required five digit number is 85041}$$

Find the sum of the greatest six-digit numbers formed by the digits $$2,0,4,7,6,5$$ using each digit only once.

Given number are $$2,0,4,7,6,5$$
Total largest number is $$=765420$$
Smallest number is $$=204567$$
$$\therefore $$ Sum of number are $$=765420+240567=969987$$

A factory has a container filled with $$35874$$ liters of cold drink. In how many bottles of $$200\ ml$$ capacity each can it be filled?

$$\textbf{Number of bottles that can be filled can be found by dividing the available cold drink with the}$$

$$\textbf{capacity of one bottle}$$.

No. of bottles $$ = \dfrac{\text{Total cold drink}}{\text{Capacity of one bottle}}$$

We know that $$1$$ Litre $$=1000\ ml$$

Therefore $$35874$$ liters $$= 35874 \times 1000\ ml$$

So, Number of bottles $$= \dfrac{35874 \times 1000}{200}$$

$$= 35874 \times 5$$

$$= 179370$$

$$\textbf{Hence, the required numbers of bottles is 179370}$$

Which one is greater ?
$$ 1 $$ meters $$ 40 $$ centimeters + $$ 60 $$ centimeters or $$ 2.6 $$ meters.

We know that $$ 1 m = 100 cm $$
$$ \therefore 1 cm = \dfrac { 1}{ 100} m $$
Now,
$$ 1 $$ Meter $$ 40 $$ centimeters + $$ 60 $$ centimeters
$$ = 1m + \dfrac {40}{100}m + \dfrac {60}{100 }m $$
$$ \Rightarrow 1m + 0.40m + 0.60 m = 2.00 m $$

A vessel has $$13$$ litres $$200\ mL$$ of fruit juice. In how many glasses each of capacity $$60\ mL$$ can it be filled?

$$\textbf{Step 1: Conversion of liters to milliliters:}$$

$$1$$ Litre $$= 1000\ mL$$

$$\therefore$$ $$13$$ Litres $$200\ mL = 13 \times 1000\ mL + 200\ mL$$

$$= 13000\ mL + 200\ mL$$

$$= 13200\ mL$$

$$\textbf{Step 2: Finding the number of glasses}$$

$$\therefore$$ $$\text{No. of glasses}$$ $$= \dfrac{\text{Capacity of the vessel}}{\text{Capacity of the glass}} $$

$$= \dfrac{13200}{60}$$

$$= 220$$

$$\textbf{Hence, the number of glasses are 220}$$

$$23 \times (-99) = $$ ____ $$\times(-100 + $$ _ $$)=23 \times $$ $$+ 23 \times $$ _

$$23 \times (-99) = $$ _$$23$$_ $$\times(-100 + $$ _1_ $$)=23 \times $$ _$$-100$$_ $$+ 23 \times $$ _1_

Estimate each of the following by rounding off each number to nearest hundreds:
$$874+478$$

Nearest hundreds round off $$874$$ is $$900$$ and round off $$478$$ is $$500$$
So, rounded the total nearest is $$=900+500=1400$$

How many lakhs make five billion?

$$\textbf{Convert billions to Lakhs}$$

$$1$$ billion $$= 1, 000, 000, 000$$

$$\therefore$$ $$5$$ billions $$= 5 \times 1, 000, 000, 000$$

$$= 5, 000, 000, 000$$

$$= 5000000000$$

$$= 50000 \times 100000$$

$$= 50000$$ Lakhs (since $$100000 = 1$$ lakh)

$$\textbf{Hence, 50, 000 Lakhs make the five billions}$$.

Estimate each of the following by rounding off each number to nearest hundreds:
$$11244+3507$$

Nearest hundreds round off $$11244$$ is $$11200$$ and round off $$3507$$ is $$3500$$
So, rounded the total nearest is $$=11200+3500=14700$$

Estimate each of the following by rounding off each number to nearest tens:
$$11963-9369$$

Nearest ten's round off $$11963$$ is $$11960$$ and round off $$9369$$ is $$9370$$

So, rounded the total nearest is $$=11960-9370=2590$$

How many millions make $$3$$ crores?

$$\textbf{Step 1: Conversion from crores to millions}$$

$$1$$ crore $$= 1,00,00,000$$

$$\therefore\ 3$$ crores $$= 3 \times 1,00,00,000$$

$$ = 30000000$$

$$ = 30 \times 1000000$$

$$= 30 \times 1$$ millions (since $$100000 = 1$$ million)

$$= 30$$ millions

$$\textbf{Hence, 30 millions make 3 crores}$$

Estimate each of the following by rounding off each number to nearest hundreds:
$$17677+13589$$

Nearest hundreds round off $$17677$$ is $$17700$$ and round off $$13589$$ is $$13600$$
So, rounded the total nearest is $$=17700+13600=31300$$

The population of a town was $$78787$$ in the year $$1991$$ and $$95833$$ in the year $$2001$$. Estimate the increase in population by rounding off each population to nearest hundreds.

$$\textbf{We round off a number to the higher side when the value in tens place is 5 or more else we round}$$

$$\textbf{it off to the lower side}$$.

Population in the year $$1991 = 78787$$

$$78787 \rightarrow$$ Ten's place $$8 > 5$$, so rounding off to the nearest hundreds $$= 78800$$

Population in the year $$2001 = 95833$$

$$95833 \rightarrow$$ Ten's place $$3 < 5$$, so rounding off to the nearest hundreds $$= 95800$$

$$\therefore$$ Increase in population $$= 95800 - 78800 = 1700$$

$$\textbf{Hence, estimated increase in population by rounding off each population to nearest hundreds}$$

$$\textbf{is 17000}$$

Estimate the following using general rule:
$$730 + 998$$
Make ten more such examples of addition, subtraction and estimation of their outcome.

$$730 + 998 :-$$
By rounding off to hundreds, $$630$$ rounds off to $$7.00$$ and $$998$$ rounds off to $$1000$$
$$700$$
$$+1000$$
$$.........$$
Total $$=1700$$
$$.........$$
The estimated value of the addition of these two number is $$1700.$$

Round off the following to the nearest tens: $$27$$.

₹ $$27$$ to the nearest ten is ₹ $$30$$.

Fill in the blanks :
In $$ 3,25,648 $$, the local value of $$ 5 $$ is .......

In $$ 3,25,648 $$, the local value of $$ 5 $$ is $$ 5 \times 1000 $$

$$ = 5000 $$

Work out following multiplication,
$$\dfrac { \begin{matrix} 123456789 \\ \times \ 9 \end{matrix} }{ } $$
Use the result to answer the following questions.
What will be $$123456789 \times 45$$?

$$\dfrac { \begin{matrix} 123456789 \\ \times \ 9 \end{matrix} }{ 1111111101 } $$

So, $$123456789\times45=123456789\times9\times5$$

$$=1111111101\times5=5555555505$$

So,

$$\dfrac { \begin{matrix} 123456789 \\ \times \ 45 \end{matrix} }{ 5555555505 } $$

Write the above as numbers in the given table.
Hundreds
$$(100)$$ Tens
$$(10)$$ Ones
$$(1)$$ Tenths
$$(\dfrac{1}{10})$$

It may be observed that

Hundred Tens Ones Tenths

a. 0 3 1 2

b. 1 1 0 4

Estimate the following using general rule:
$$28,292 - 21,496$$

$$28,292 - 21,496 :-$$

By rounding off to nearest thousands, $$28296$$ rounds off to $$28000$$ and $$21496$$ rounds off to $$21000$$

$$28000$$

$$-21000$$

$$........$$

$$7000$$

$$........$$

The difference of these two numbers is $$7000.$$

Work out following multiplication,
$$\dfrac { \begin{matrix} 123456789 \\ \times \ 9 \end{matrix} }{ } $$
Use the result to answer the following questions.
By what number should $$123456789 $$ be multiplied to get $$9999999909$$?

$$\dfrac { \begin{matrix} 123456789 \\ \times \ 9 \end{matrix} }{ 1111111101 } $$

$$9999999909=1111111101\times9$$

$$\Rightarrow 9999999909=123456789\times9\times9$$

$$\Rightarrow 9999999909=123456789\times81$$

By $$81$$ number should $$123456789 $$ be multiplied we get $$9999999909$$

Express the following in the standard form :
Express $$56\ km$$ in $$m$$.

Given, $$56\ km=56\times 1000\ m=56000\ m$$
Standard form of -
$$56000\ m=56\times 10^3=5.6\times 10^3 \times 10^1=5.6\times 10^4\ m$$

Add (giving answer in kg):
$$778 gm$$ and $$1.939 kg$$

$$778 gm$$ and $$1.939 kg$$
First convert the $$778 gm$$ into $$kg$$
We get,
$$= 778 / 100 kg + 1.939 kg$$
$$= 7.78 kg + 1.939 kg$$
Converting the decimals into like decimals
We get,
$$= 0.778 kg + 1.939 kg$$
$$= 2.717 kg$$
$$\therefore$$ The addition of $$778 gm$$ and $$1.939 kg$$ is $$2.717 kg$$

The Patel family flies from their home town, H, to Kiruna , K , in Lapland.
Mr. Patel buys a bag of sweets.
The bag of sweets costs $$ $ 3.25$$.
Calculate the cost of the sweets in euros $$(\in)$$ when the exchange rate is $$\in1 = $1.24$$.

Cost of the sweets is $ $$3.25$$

Given $$\in 1=$1.24$$

Thus, cost of sweets in Euros is given by,

$$C=\frac { 3.25 }{ 1.24 } $$

$$\therefore C=\in 2.62$$

Add the following rational number
$$\dfrac{-3}{7}$$ and $$\dfrac{-5}{7}$$

Add $$\cfrac{-3}{7}$$ and $$\cfrac{-5}{7}$$

$$\cfrac{-3}{7}+(\cfrac{-5}{7})$$

$$\cfrac{-3+(-5)}{7}=\cfrac{-3-5}{7}=\cfrac{-8}{7}$$

Knowing Our Numbers - Class 6 Maths - Extra Questions

Subtract: $$3xy + 5yz- 7zx$$ from $$5xy -2yz- 2zx + 10xyz$$

Four numbers $$3, 1, 2$$ and $$5$$ are given. Form a four digit number from these given numbers such that the digits in the final number are in increasing order.

Bhanu bought 3 kg 500 gm of jalebi, 2 kg 250 gm of Mysore Pak and 1 kg 750 gm badhushaw, and 750 gm of Jamun. What is the total weight of the sweets that Bhanu bought?

Compute the following:$$100+(-80)$$

Compute the following:$$14+(-10)$$

Compute the following:$$225+(-145)$$

Compute the following:$$10+(-2)$$

Compute the following:$$13+(-15)$$

How many dozen bananas are there in 216 bananas?

Compute the following:$$7+4$$

In its search for water a frog fell down into a $$30m$$ deep well. Its progress out of the well was very erratic. Each day it managed to climb up $$3\ m$$, but the following night , it slipped back $$2\ m$$. How many days did it take to get out of the well?

Solve the following:$$80-(-50)$$

Fill in the following blanks:_____ $$ \div 1=-49$$

Solve the following:$$32-(-18)$$

Write the number names according to :NumberIndian SystemInternational system23674948670002

Solve the following:$$150-75$$

Solve the following:$$25-33$$

Add $$48 + 49 + 31 + 30 = \_\_\_\_\_$$

How many five thousands are there in one lakh?

The number $$6778243$$ should properly be written as_______________

Solve $$5+(-4)+1$$

Add $$48$$+$$49$$+$$31$$+$$30$$

Subtract the sum of $$-1032$$ and $$878$$ from $$-34$$.

Subtract $$635$$ from $$-547$$

Arrange in ascending order.$$\dfrac{14}{25}, \dfrac{18}{27}, \dfrac{16}{21}, \dfrac{12}{24}, \dfrac{17}{29}$$

Mohit travelled in a bus towards $$east$$ $$of$$ $$Delhi$$ by $$49km$$ then towards $$west$$ $$of$$ $$Delhi$$ by $$80km$$. How far was he from Delhi?

Fill in the blanks with $$<$$ or $$>$$ sign.$$34512$$ ________ $$5451$$.

Which is the bigger and which the smaller number?$$423\ \Box\ 723$$

Simplify:$$28-3\times 5+4$$$$42-18\div 2\times 3$$

Which is the bigger and which the smaller number?$$721\ \Box\ 589$$

Simplify$$\sqrt{50}-\sqrt{98}$$

Rama left her home on the morning of $$11.11.2015$$ and came back home at the night of $$12.12.2016$$. For how many days was she remain away from home.

Simplify:$$\cfrac{27}{9}+(27-1)\cfrac{9}{27}$$

$$LXXXI$$= _______ (Write the value in Hindu - Arabic number,)

Write the Roman numerals for the following:$$94$$

Find the value of x $$\cfrac { 17.28\div x }{ 3.6\times 0.2 } =2$$

Write the Roman numerals for the following:$$550$$

What should be added to $$(2\cfrac{1}{3}+2\cfrac{2}{5})$$ to get the sum $$10$$?

Solve $$\dfrac{2}{7} - \left( {\dfrac{{ - 5}}{6}} \right)$$

Write the Roman numerals for the following:$$260$$

Write the Roman numerals for the following:$$900$$

Write the Roman numerals for the following:$$120$$

Madhu buys $$5\ kg$$ of potatoes at the market. If the cost of $$2\ kg$$ is $$Rs. 36$$, how will Madhu pay?

Subtract the sum of $$1\cfrac{7}{10}$$ and $$2\cfrac{1}{5}$$ from $$5$$

Add $$6\frac{2}{3} + 4\frac{3}{5}$$ and subtract $$4\frac{2}{7} - 3\frac{3}{7}$$

Solve : $$2a - [4b - \{4a - (3b - \overline{2a + 2b})\}]$$

Subtract the sum of $$-48$$ and $$-58$$ from $$102$$.

If $$a = 2$$ and $$b = 3$$, find the value of $$a + b$$.

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$3x - 2y + z$$.

If $$a = 2$$ and $$b = 3$$, find the value of $$5a^{2} - 2ab$$.

If $$a = 2$$ and $$b = 3$$, find the value of $$a^{3} - b^{3}$$.

If $$a = 2$$ and $$b = 3$$, find the value of $$2a - 3b$$.

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$2x^{2} y - 5yz + xy^{2}$$.

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$xy + yz - zx$$.

If $$x = 1, y = 2$$ and $$z = 5$$, find the value of $$x^{3} - y^{3} - z^{3}$$.

Verify the following: $$\left (-13\right)x\left[\left(-6\right)+\left (-19\right)\right]=\left (-13\right)x\left (-6\right)+\left (-13\right)x\left (-19\right)$$.

Evaluate:$$\dfrac {7}{13}+\dfrac {-4}{39}$$

Express in Roman numerals :i) $$105$$ii) $$511$$

What should be added to $$729.28$$ to get $$1000$$?

Subtract $$0.5-0.49$$

$$1$$ million $$=$$ ____ hundred thousands.

The sum of two numbers is $$30.64$$. If one of the numbers is $$21.28$$, find the other.

Substact the sum of $$\dfrac{2}{7}$$ and $$-\dfrac{4}{21}$$ from $$\dfrac{1}{21}$$

Rahul bought $$1.5\ kg$$, Govind bought $$7.25\ kg$$ and Rakesh bought $$18\ kg$$ of wheat. What is the total quantity of wheat bought by them altogether?

Aneeta gave $$Rs. 2099.99$$ to her sister and $$Rs. 1991.11$$ to her brother. How much amount did she give in all?

Estimate the value of $$500+80+2+\dfrac{1}{10}+\dfrac{0}{100}+\dfrac{7}{1000}$$.

Estimate the value of $$2000+0+70+3+\dfrac{2}{10}+\dfrac{6}{100}$$.

Fill in the blank space.19 + ____ = 42

Find the value of $$\dfrac {1}{2}+3 +\dfrac {1}{2}-3$$.

Simplify:-$$4\frac{1}{2} - 1\frac{4}{5}$$

Find the solution of the following:$$(-9)+(+13)$$

How much is 90-19?

The sum of the least number of three digits and largest number of two digits is .......

Solve : m cm $$5$$ $$12$$ + $$3$$ $$46$$ _________________

Subtract:(a) $$18$$ rupees $$9$$ paise from $$75$$ rupees $$80$$ paise.(b) $$49$$ rupees $$79$$ paise from $$123$$ rupees $$68$$ paise.

Simplify: i) $$45 + (-12) - 12 $$ii) $$123 + 89 - (-11)$$iii) $$-85 - 15 + 200$$iv) $$96 + (-16) - (-20) $$v).$$ 36 - (-14) + 25 $$vi) $$155 + (-25) + 50$$vii) $$23 + (-56) - (-56) $$viii) $$45 - 85 - 15 + (-25)$$ix) $$78 - 39 + (-19) - (-29) $$x) $$450 - 255 + (-230) + 560 $$

Solve :$$(5+(-3)+6)$$

Which is the largest $$3$$ digit number ?

Estimate $$5(10+1)$$

Subtract:
$$3xy + 5yz- 7zx$$ from $$5xy -2yz- 2zx + 10xyz$$

Compute the following:
$$100+(-80)$$

Compute the following:
$$14+(-10)$$

Compute the following:
$$225+(-145)$$

Compute the following:
$$10+(-2)$$

Compute the following:
$$13+(-15)$$

Compute the following:
$$7+4$$

Solve the following:
$$80-(-50)$$

Fill in the following blanks:
_____ $$ \div 1=-49$$

Solve the following:
$$32-(-18)$$

Write the number names according to :
Number Indian System International system
236749
48670002

Solve the following:
$$150-75$$

Solve the following:
$$25-33$$

Arrange in ascending order.
$$\dfrac{14}{25}, \dfrac{18}{27}, \dfrac{16}{21}, \dfrac{12}{24}, \dfrac{17}{29}$$

Fill in the blanks with $$<$$ or $$>$$ sign.
$$34512$$ ________ $$5451$$.

Which is the bigger and which the smaller number?
$$423\ \Box\ 723$$

Simplify:
$$28-3\times 5+4$$
$$42-18\div 2\times 3$$

Which is the bigger and which the smaller number?
$$721\ \Box\ 589$$

Simplify
$$\sqrt{50}-\sqrt{98}$$

Simplify:
$$\cfrac{27}{9}+(27-1)\cfrac{9}{27}$$

Write the Roman numerals for the following:
$$94$$

Write the Roman numerals for the following:
$$550$$

Write the Roman numerals for the following:
$$260$$

Write the Roman numerals for the following:
$$900$$

Write the Roman numerals for the following:
$$120$$

Evaluate:
$$\dfrac {7}{13}+\dfrac {-4}{39}$$

Express in Roman numerals :
i) $$105$$
ii) $$511$$

Fill in the blank space.
19 + ____ = 42

Simplify:-
$$4\frac{1}{2} - 1\frac{4}{5}$$

Find the solution of the following:
$$(-9)+(+13)$$

Solve :
m cm
$$5$$ $$12$$
+ $$3$$ $$46$$
_________________

Subtract:
(a) $$18$$ rupees $$9$$ paise from $$75$$ rupees $$80$$ paise.
(b) $$49$$ rupees $$79$$ paise from $$123$$ rupees $$68$$ paise.

Simplify:
i) $$45 + (-12) - 12 $$
ii) $$123 + 89 - (-11)$$
iii) $$-85 - 15 + 200$$
iv) $$96 + (-16) - (-20) $$
v).$$ 36 - (-14) + 25 $$
vi) $$155 + (-25) + 50$$
vii) $$23 + (-56) - (-56) $$
viii) $$45 - 85 - 15 + (-25)$$
ix) $$78 - 39 + (-19) - (-29) $$
x) $$450 - 255 + (-230) + 560 $$

Solve :
$$(5+(-3)+6)$$

PErform the give operation:
$$77+888$$
$$9999-1$$

Fill in.
In $$7362, 3$$ is in the__place and $$7$$ is in the place.

Place commas correctly and write the numerals:
Nine crore five lakh forty one.

Fill in the blank.
$$1$$ lakh $$=$$ _______ ten thousand.

Fill in the blank.
$$1$$ million $$=$$_______ lakh.

Place commas correctly and write the numerals.
Seven crore fifty two-lakh twenty one thousand three hundred two.

Place commas correctly and write the numerals:
Seventy three lakh seventy five thousand three hundred seven.

Insert commas suitably and write the names according to International System of Numeration:
$$7452283$$.

Give a rough estimate(by rounding off to nearest hundreds) and also a closer estimate(by rounding off to nearest tens):
$$4,89,348-48,365$$.

Estimate the following using general rule.
$$12,904+2,888$$.

Give a rough estimate(by rounding off to nearest hundreds) and also a closer estimate(by rounding off to nearest tens):
$$439+334+4,317$$.

Round these numbers to the nearest tens.
$$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936$$.

Estimate the following using general rule.
$$796-314$$.

Place commas correctly and write the numerals.
Twenty three lakh thirty thousand ten.

A bus started its journey and reached different places with a speed of $$60$$ km/hour. The journey is shown in given figure.

Find the total distance covered by the bus from A to D.

Insert commas suitably and write the names according to International System of Numeration:
$$78921092$$.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign $$(>, <)$$ between them.
$$530$$, $$503$$.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also written them with the appropriate sign $$(>, <)$$ between them.
$$98765$$, $$56789$$.

In the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign $$(>, <)$$ between them.
$$370$$, $$307$$.

Express the following numbers in standard form:
$$3908.78$$

Write in Roman numerals.
$$92$$.

Write in Roman numerals.
$$73$$.

Round off the following number to nearest hundreds.
$$7,289$$.

Write the roman-numerals for the following.
$$76$$.

Write the roman-numerals for the following.
$$48$$.

Round off the following number to nearest hundreds.
$$4,20,387$$.

Round off the following number to the nearest thousand.
$$20,963$$.

Write the following in Roman numerals.
$$154$$.

Estimate the following by rounding off the number to its greatest place.
$$1,08,734-47,599$$.

Estimate the following by rounding off the number to its greatest place.
$$9\times 795$$.

Round off the following number to nearest hundreds.
$$14,627$$.

Round off the following number to nearest hundreds.
$$8,074$$.

Estimate the following by rounding off the number to its greatest place.
$$87\times 317$$.

Fill in the blank with the appropriate symbol $$<$$ or $$>$$.
$$170$$____$$107$$.

Estimate the difference to the nearest thousand:
$$(47005 - 39488)$$

Round the following number to the nearest thousand:
$$28394$$

Round the following number to the nearest ten thousand:
$$17514$$

Estimate the difference to the nearest thousand:
$$(35863 - 27677)$$

Express the following as a Roman numeral:
$$2$$

Write the following in Roman numerals.
$$319$$.

Arrange the following numbers in descending order:
$$8435,\ 4835,\ 13584,\ 5384,\ 25843$$

Write the following decimal in expanded form:
$$4615.72 $$

Estimate each of the following by rounding off each number to nearest tens:
$$10732-4354$$

Find the smallest and the greatest numbers in each case given below:
$$983, 5754, 84$$ and $$5942$$

By making a suitable chart, compare:
$$540276$$ and $$369998$$

By making a suitable chart, compare:
$$6983245$$ and $$6893254$$