Question

Express the following as a rational number i.e in the form $\frac{a}{b}$; where $a,b\in I$ and $b\ne 0$.
$0.5\overline{3}$

• A. $\frac{8}{15}$
• B. $\frac{8}{13}$
• C. $\frac{8}{11}$
• D. $\frac{8}{19}$

Answer 1

The correct option is A $\frac{8}{15}$

Let $x=0.5\overline{3}$

$\Rightarrow x=0.5333...\left(1\right)$

Multiply $\left(1\right)$ by $10$ we get

$10x=5.333...\left(2\right)$

Subtract $\left(2\right)$ and $\left(1\right)$ we get

$10x-x=5.3333-0.5333$

$\Rightarrow 9x=4.8$

$\Rightarrow 9x=\frac{24}{5}$

$\Rightarrow x=\frac{24}{45}$

$\Rightarrow x=\frac{8}{15}$

$\therefore 0.5\overline{3}=\frac{8}{15}$