Question

How do you convert $0.36$($36$ repeating) to a fraction?

Answer 1

Convert decimal to a fraction:

The given decimal number is $0.36$(36 repeating).

Let the given decimal number be equal to x. Then,

$x=0.3636363636....$ (Let this equation be equation $1$)

Multiply equation $1$ by $100$.

$\Rightarrow 100x=36.363636.....$ (Let this equation be equation $2$)

Subtract equation $2$ from equation $1$ and simplify to get the required fraction.

$$\begin{gathered} 100x-x=36.363636....-0.363636.... \\ 99x=36 \\ x=\frac{36}{99} \\ x=\frac{4}{11} \end{gathered}$$

Hence, the given decimal can be written as $4over11$.