Question

Convert $0.08\overline{3}$ into $\frac{p}{q}$ form.

• A. $\frac{1}{12}$
• B. $\frac{1}{14}$
• C. $\frac{1}{16}$
• D. $\frac{1}{23}$

Answer 1

The correct option is A

$\frac{1}{12}$

Multiply $0.08\overline{3}$ by $100$ so as to make the decimal point just before the recurring digit which in this case is $3.$

So, let $x=\mathrm{8.3333...}$ (i)

$10x=\mathrm{83.3333...}$ (ii)

Subtracting (i) from (ii)

$9x=\mathrm{83.3333...}-\mathrm{8.33333...}=75$

$\Rightarrow x=\frac{75}{9}$

So, $0.08\overline{3}=\frac{75}{900}=\frac{1}{12}$