Question:
The simplest for of $1 . \overline{6}$ is
(a) $\frac{833}{500}$
(b) $\frac{8}{5}$
(C) $\frac{5}{3}$
(d) none of these
Solution:
(C) $\frac{5}{3}$
Let x = 1.6666666... ...(i)
Multiplying by 10 on both sides, we get:
10x = 16.6666666... ...(ii)
Subtracting (i) from (ii), we get:
9x = 15
$\Rightarrow x=\frac{15}{9}=\frac{5}{3}$