Question

The simplest form of $1.\overline{6}$ is

(a)$\frac{833}{500}$

(b)$\frac{8}{5}$

(c)$\frac{5}{3}$

(d) none of these

Answer 1

(c) $\frac{5}{3}$

Let $x=\mathrm{1.6666666...}$ ------(i)

Multiplying by 10 on both sides, we get:

$10x=\mathrm{16.6666666..}$------(ii)

Subtracting (i) from (ii), we get:

$9x=15\Rightarrow x=\frac{15}{9}=\frac{5}{3}$