Question

Which of the following has a terminating decimal ?
(i) $\frac{2}{3}$
(ii) $\frac{1}{3}$
(iii) $\frac{1}{9}$
(iv) $\frac{1}{5}$

Answer 1

$\frac{2}{3}$ = 0.666....Non terminating decimal
$\frac{1}{3}$ = 0.333.....Non terminating decimal
$\frac{1}{9}$ = 0.1111......Non terminating decimal
$\frac{1}{5}$ = 0.2 which is the only terminating decimal.

The denominators of (a), (b) and (c) are not in the form $2^n{5}^m$, where n and m are positive integers.

$\therefore$ They have non-terminating decimal expansions.