Explanation
$${\textbf{Step - 1: Checking option - A}}{\text{.}}$$
$${\text{We have 0}}{\text{.54 in the first option}}{\text{.}}$$
$${\text{0}}{\text{.54 is clearly a rational number as it can be written in the form }}\dfrac{p}{q}{\text{ as }}\dfrac{{54}}{{100.}}$$
$${\textbf{Step - 2: Checking option - B}}{\text{.}}$$
$${\text{We have }}6.\overline{54}{\text{ in the second option}}{\text{.}}$$
$${\text{As 6}}.\overline{54}{\text{ is a non - terminating recurring decimal, and as we know that }}$$
$${\text{non - terminating recurring decimal are rational, therefore, it is also a rational number}}{\text{.}}$$
$${\textbf{Step - 3: Checking option - C}}{\text{.}}$$
$${\text{Here we have }}0.\overline {1416}{\text{ , so this is also a non - terminating recurring decimal}}{\text{.}}$$
$${\text{Therefore, it also a rational number}}{\text{.}}$$
$${\textbf{Step - 4: Checking option - D}}{\text{.}}$$
$${\text{Here we have }}0.4014001400014...{\text{ which we can see is a non - terminating,}}$$
$${\text{non - recurring decimal}}{\text{. Therefore, it is an irrational number}}{\text{.}}$$
$${\textbf{Hennce, The decimal in option - D is an irrational number}}{\text{.}}$$
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