Question

Which of the following is/are a rational number?

• A. $\mathrm{1.2345...}$
• B. $\mathrm{1.20200200...}$
• C. $\frac{5}{10}$
• D. $\mathrm{1.333...}$

Answer 1

Answer: (C), (D)

$\mathrm{1.333...}$

The number that can be expressed in the $\frac{p}{q}$, where $p\&q$ are integers and $q\ne 0$, is rational number.

Rational numbers are either terminating decimals or non-terminating repeating decimals.

$\mathrm{1.2345...}$ is a non-terminating non-repeating decimal, hence it is not a rational number.

$\mathrm{1.20200200...}$ is a non-terminating non-repeating decimal, hence it is not a rational number.

$\frac{5}{10}=0.5$ is a rational number.

$\mathrm{1.333...}=1+\mathrm{0.33...}$

We know that $\frac{1}{3}=\mathrm{0.33...}$

$\therefore \mathrm{1.333...}=1+\mathrm{0.33...}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}$

Hence, $\mathrm{1.33...}$ is also a rational number.