Question

What is $0.\overline{75}$ written as a fraction?

Answer 1

Step 1: $0.\overline{75}$ written as a fraction:

Let

$$\begin{gathered} x=0.\overline{75} \\ x=0.757575....\left(1\right) \end{gathered}$$

Step 2: Multiply with 100 on both sides

$100x=75.75....\left(2\right)$

Subtract equation 1 from equation 2

$$\begin{gathered} 100x-x=75.7575....-0.757575.... \\ 99x=75 \end{gathered}$$

So,

$x=\frac{75}{99}=\frac{25}{33}$

Hence, the required fraction form is $\frac{25}{33}$.