Question

Which 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 contains only 2 and 5. Otherwise, the fraction is non-terminating and repeating. For e.g.
The prime factors of 250, 25 and 32 in option A, B and C respectively contain only 2 and 5.
$250=2\times 5^3$, thus $\frac{3}{250}=0.012$ (terminating decimal)
$25=5^2$, thus $\frac{7}{25}=0.28$ (terminating decimal)
$32=2^5$, thus $\frac{17}{32}=0.53125$ (terminating decimal)
$36=2^2\times 3^2$, thus $\frac{17}{36}=\mathrm{0.47222....}$ .(non-terminating and repeating decimal)