Question

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

• A. $\frac{17}{16}$
• B. $\frac{83}{25}$
• C. $\frac{28}{9}$
• D. $\frac{22}{32}$

Answer 1

The correct option is C

$\frac{28}{9}$

$\frac{17}{16}$ = 1.0625

$\frac{83}{25}$ = 3.32

$\frac{22}{32}$ = 0.6875

Only the fraction $\frac{28}{9}$ has a recurring and non-terminating decimal number whose value is 3.1111...
The other fractions are terminating decimal numbers.

Note - If on simplifying a fraction, in the denominator we have only multiple of 2 or 5 or both then the fraction will always be a terminating decimal.