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

Answer 1

(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
∴ x = $\frac{29}{90}$