# The simplest form of

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

Solution:

(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

$\Rightarrow x=\frac{54}{99}=\frac{6}{11}$