Question

Among the given options, is a non-terminating and repeating decimal.

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

Answer 1

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

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

The prime factors of 25 and 32 in $\frac{7}{25}$ and $\frac{17}{32}$ respectively contain only 2 and 5.
$25=5^2$, thus $\frac{7}{25}=0.28$ (terminating decimal)
$32=2^5$, thus $\frac{17}{32}=0.53125$ (terminating decimal)

In $\frac{17}{36}$, $36=2^2\times 3^2$, thus $\frac{17}{36}=\mathrm{0.47222....}$ (non-terminating and repeating decimal)