Question

The number $0.3\overline{2}$ in the form $p/q$, where $p$ and $q$ are integers and $q\ne 0$, is

• A. $\frac{8}{25}$
• B. $\frac{32}{199}$
• C. $\frac{29}{90}$
• D. $\frac{32}{99}$

Answer 1

The correct option is C $\frac{29}{90}$

Let $x=0.3\overline{2}=0.3222$….(i)
$\Rightarrow 10x=3.222\dots$(ii)
$\Rightarrow 100x=32.222\dots$(ii)
Subtracting equation (ii) from equation (iii), we get
$90x=29$
$\Rightarrow x=\frac{29}{90}$