Question

Express the given decimal expression in the form of $\frac{p}{q}$.

(i).$0.\overline{8}$

Answer 1

Solution:

Expressing in $\frac{p}{q}$form:

Let $x=0\overline{.8}=0.8888.........\left(1\right)$

$\Rightarrow 10\mathrm{x}=8.888.......\left(2\right)\left[\mathrm{Equation}\left(1\right)\mathrm{is}\mathrm{multiplied}\mathrm{by}10\right]$

Subtracting equation (1) from (2):

$$\begin{gathered} \Rightarrow 10x-x=8.888...-0.8888.... \\ \Rightarrow 9x=8 \\ \Rightarrow x=\frac{\mathbf{8}}{\mathbf{9}} \end{gathered}$$

Final answer: Hence, the $\frac{p}{q}$ form of the given decimal number is$\frac{\mathbf{8}}{\mathbf{9}}$.