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 $x=\mathrm{0.3222222222...}$----(i)

Multiplying by 10 on both sides, we get:

$10x=\mathrm{3.222222222...}$ ----(ii)

Again, multiplying by 10 on both sides, we get:

$100x=\mathrm{32.222222222...}$----(iii)

On subtracting (ii) from (iii), we get:

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