Question

Every repeating decimal is a rational number.

• A. True
• B. False

Answer 1

The correct option is A True

1. A number is rational if it can be written as $\frac{p}{q}$, where $pandq$ are integers and $q\ne 0$.
2. Repeating decimals are decimal representations of numbers with infinitely repeating digits.
3. Numbers with a repeating pattern of decimals (having same number/s repeating on expansion after decimal point) are rational because when we put them into fractional form, both the numerator $p$ and denominator $q$ become non-fractional whole numbers.
4. Example: $0.\overline{3}=\frac{1}{3}$

Hence, the given statement is true.