Question

Convert the decimal $0.272727\dots$ into a fraction.

• A. $\frac{3}{11}$
• B. $\frac{3}{8}$
• C. $\frac{3}{10}$
• D. $\frac{3}{13}$

Answer 1

The correct option is A $\frac{3}{11}$

Let, $m=\mathrm{0.272727...}\dots \left(i\right)$

Here, $27$ is the two digit number that is repeating itself after the decimal point.So, multiply both the sides by $100$ ,not by $10$ .

$\Rightarrow 100m=\mathrm{27.272727...}\dots \left(ii\right)$

By substracting equation $\left(i\right)$ from $\left(ii\right)$,we get

$\Rightarrow 100m-m=\mathrm{27.2727...}-\mathrm{0.272727...}$
$\Rightarrow 99m=27$
$\Rightarrow m=\frac{27}{99}$
$\Rightarrow m=\frac{9\times 3}{9\times 11}$

By canceling both the numerator and denominator, we get
$\Rightarrow m=\frac{3}{11}$