Which of the following is irrational?

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(D) number is irrational if and only if its decimal representation is non-terminating and non-recurring.$(A)$ $0.14$ is a terminating decimal,so it is

Vedclass · Accepted Answer

$0.4014001400014 \ldots$

Vedclass · Answer

(D) number is irrational if and only if its decimal representation is non-terminating and non-recurring.$(A)$ $0.14$ is a terminating decimal,so it is a rational number.$(B)$ $0.14 \overline{16}$ is a non-terminating and recurring decimal,so it is a rational number.$(C)$ $0. \overline{1416}$ is a non-terminating and recurring decimal,so it is a rational number.$(D)$ $0.4014001400014 \ldots$ is a non-terminating and non-recurring decimal,which is the definition of an irrational number.Hence,$(D)$ is the correct answer.

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