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 $x=\mathrm{0.5333...}$ ---- (1)
Then $10x=\mathrm{5.3333....}$ ------ (2)
Subtracting (1) from (2),
$10x-x=5.3333-0.5333$
$9x=4.8$
$x=\frac{4.8}{9}=\frac{48}{10\times 9}=\frac{8}{15}$