Question

Which among the following fractions (when expressed in decimals) is a recurring and non-terminating decimal?
$\frac{24}{64}$, $\frac{83}{25}$, $\frac{28}{9}$, $\frac{22}{32}$ $\left[1\text{Mark}\right]$

Answer 1

$\frac{24}{64}$ = $\frac{3}{8}$ = $\frac{3\times 125}{8\times 125}$ = 0.375 is a terminating decimal

$\frac{83}{25}$ = $\frac{83\times 4}{25\times 4}$ = $\frac{332}{100}$ = 3.32 is a terminating decimal

$\frac{22}{32}$ = $\frac{11\times 625}{16\times 625}$ = $\frac{6875}{10000}$ = 0.6875 is a terminating decimal

$\frac{28}{9}$ = 3.1111 is a recurring and non-terminating decimal number