Question

Convert $0.41\overline{6}$ into $\frac{p}{q}$ form.

• A. $\frac{5}{12}$
• B. $\frac{5}{11}$
• C. $\frac{1}{12}$
• D. $\frac{1}{11}$

Answer 1

The correct option is A

$\frac{5}{12}$

Multiply $0.41\overline{6}$ by $100$ so as to make the decimal point just before the recurring digit which in this case is $6.$

So, let $x=\mathrm{41.6666...}$ (i)

$10x=\mathrm{416.6666...}$ (ii)

Subtracting (i) from (ii),

$9x=\mathrm{416.6666...}-\mathrm{41.6666...}=375$

$\Rightarrow x=\frac{375}{9}$

So, $0.41\overline{6}=\frac{375}{9\times 100}=\frac{375}{900}=\frac{5}{12}$