Question

The simplest form of 0.12$\overline{3}$ is

(a)$\frac{41}{330}$ (b)$\frac{37}{330}$ (c)$\frac{41}{333}$ (d) none of these

Answer 1

(d) none of these

Let $x=\mathrm{0.12333333333...}$----(i)

Multiplying by 100 on both sides, we get:

$100x=\mathrm{12.33333333...}$----(ii)

Multiplying by 10 on both sides, we get:

$1000x=\mathrm{123.33333333...}$----(iii)

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

$900x=111\Rightarrow x=\frac{111}{900}$