The simplest form of
Question:

The simplest form of $0.3 \overline{2}$ is

(a) $\frac{16}{45}$

(b) $\frac{32}{99}$

(c) $\frac{29}{90}$

(d) none of these

Solution:

(c) $\frac{29}{90}$

Let x = 0.3222222222…          …(i)
Multiplying by 10 on both sides, we get:
10x = 3.222222222…              …(ii)
Again, multiplying by 10 on both sides, we get:
100x = 32.222222222…          …(iii)
On subtracting (ii) from (iii), we get:
90x = 29

$\therefore x=\frac{29}{90}$