Question

Among the following, the terminating rational number is .

• A. $\frac{1}{8}$
• B. $\frac{1}{13}$
• C. $\frac{1}{11}$

Answer 1

The correct option is A $\frac{1}{8}$

A decimal is terminating only when the denominators can be prime factored in the form of
$2^m\times 5^n$.

If the denominator has any other prime factor, then the decimal becomes non-terminating and repeating.

$\text{In}\frac{1}{8},\text{8 is equivalent to}{2}^3\times 5^0.$ Hence, it is terminating.

$\text{In}\frac{1}{13},\text{13 cannot be expressed}\text{in the form of}{2}^m\times 5^n.\text{Hence, it}\text{is non terminating and repeating.}$

$\text{In,}\frac{1}{11},\text{11 cannot be expressed}\text{in the form of}{2}^m\times 5^n.\text{Hence, it}\text{is non terminating and repeating.}$