Question

Non terminating and repeating rational number from among the following is .

• A. $\frac{3}{8}$
• B. $\frac{1}{7}$
• C. $\frac{1}{10}$

Answer 1

The correct option is B $\frac{1}{7}$

A decimal is terminating only when the denominators can be prime factored in the form of $2^m\times 5^n$.
$\frac{3}{8}$ = 0.375 which is terminating. Here 8 is equivalent to $2^3$. Hence, it is terminating.
$\frac{1}{10}$ = 0.1 which is terminating. Here 10 is equivalent to $2^1\times 5^1$. Hence, it is terminating.
Whereas, in $\frac{1}{7}$ , 7 cannot be expressed in the form of $2^m\times 5^n$. Hence, it is non terminating and repeating.