Question

of the following rational numbers is a non-terminating and repeating decimal.

• A. $\frac{3}{250}$
• B. $\frac{7}{25}$
• C. $\frac{17}{32}$
• D. $\frac{17}{36}$

Answer 1

The correct option is D $\frac{17}{36}$

A fraction is terminating only when the prime factors of denominator are only 2 and 5. Otherwise, the fraction is non-terminating and repeating.

For example:
The prime factors of 250, 25 and 32 contain only 2 and 5.

$250=2\times 5^3\text{Thus,}\frac{3}{250}=0.012\text{is a terminating}\text{decimal.}$

$25=2^0\times 5^2,\text{Thus,}\frac{7}{25}=0.28\text{is a terminating}\text{decimal.}$

$32=2^5\times 5^0\text{Thus,}\frac{17}{32}=0.53125\text{is a terminating}\text{decimal.}$

$36=2^2\times 3^2\text{Thus,}\frac{17}{36}=\mathrm{0.47222...}\text{non-terminating}\text{and repeating decimal.}$