Question

Which of the following fractions is a recurring and non-terminating decimal?

• A. $\frac{24}{64}$
• B. $\frac{83}{25}$
• C. $\frac{28}{9}$
• D. $\frac{22}{32}$

Answer 1

The correct option is C

$\frac{28}{9}$

$\frac{24}{64}$ = $\frac{3}{8}$ = $\frac{3\times 125}{8\times 125}$= 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 has a recurring and non-terminating decimal number