Question

The simplest form of $0.\overline{54}$ is
(a) $\frac{27}{50}$
(b) $\frac{6}{11}$
(c) $\frac{4}{7}$
(d) none of these

Answer 1

(b) $\frac{6}{11}$
Let x = 0.545454... ...(i)
Multiplying both sides by 100, we get:
100x = 54.5454545... ...(ii)
Subtracting (i) from (ii), we get:
99x = 540
$\Rightarrow$x = $\frac{54}{99}$ = $\frac{6}{11}$