Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
5 (3)

Answer 1

It is written as $\mathrm{5.33333333333......}$

Now let $x=\mathrm{5.33333333......}$ $\left(1\right)$

Multiply equation $\left(1\right)$ by $10$ on both sides, we get

$10\times x$ $=\mathrm{5.333333333...}\times 10$

$10x=\mathrm{53.333333333...........}$ $\left(2\right)$

Now subtract $\left(1\right)$ from $\left(2\right)$, we have

$10x-x=53.3333333333-5.3333333$

$\Rightarrow 9x=48$

$\Rightarrow x=\frac{48}{9}$