Question

How do you convert $0.8(8\text{repeating})$ to a fraction.

Answer 1

Converting $0.8(8\text{repeating})$ to a fraction :

Let, $x=0.8888....\dots \left(1\right)$

Multiplying $10$ both sides,

$\Rightarrow 10x=8.8888.......\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$.

$$\begin{gathered} \Rightarrow 10x-x=8.8888...-0.8888... \\ \Rightarrow 9x=8 \end{gathered}$$

$\Rightarrow x=\frac{8}{9}$

Hence, the value of $0.8(8\text{repeating})$ in fraction is $\frac{8}{9}$.