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
Solution:
(d) none of these
Let x = 0.12333333333... ...(i)
Multiplying by 100 on both sides, we get:
100x = 12.33333333... ...(ii)
Multiplying by 10 on both sides, we get:
1000x = 123.33333333... ...(iii)
Subtracting (ii) from (iii), we get:
900x = 111
$\Rightarrow x=\frac{111}{900}$