Question

How do you write $0.888...$ ($8$ repeating) as a fraction?

Answer 1

Converting the given decimal to fraction:

Consider, $x=0.\overline{8}\left(i\right)$.

Multiplying $x$ by $10$; we get,

$10x=8.\overline{8}\left(ii\right)$

Subtracting $x$ from $10x$:

$\begin{array}{rcl}10x-x& =& 8.\overline{8}-0.\overline{8}\\ & \Rightarrow & 9x=8\\ & \Rightarrow & x=\frac{8}{9}\end{array}$

Therefore, the fraction form of the given decimal, $\mathbf{0}\mathbf{.}\overline{\mathbf{8}}\mathbf{=}\frac{\mathbf{8}}{\mathbf{9}}$.