Which of the following is irrational?

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Question

A number is irrational if and only of its decimal representation is non-terminating and non-recurring.

(a) 0.14 is a terminating decimal and theref

Vedclass · Accepted Answer

$0.4014001400014 \ldots$

Vedclass · Answer

A number is irrational if and only of its decimal representation is non-terminating and non-recurring.

(a) 0.14 is a terminating decimal and therefore cannot be an irrational number.

(b) $0.14 \overline{16}$ is a non-terminating and recurring decimal and therefore cannot be irrational.

(c) $0. \overline{1416}$ is a non-terminating and recurring decimal and therefore cannot be irrational.

(d) 0.4014001400014 ... is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, $(d)$ is the correct answer.

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