Question

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

(ii).$2.\overline{4}$

Answer 1

Solution:

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

Let $\mathrm{x}=2.\overline{4}=2.444.........\left(1\right)$

$\Rightarrow 10\mathrm{x}=24.444........\left(2\right)\left[\mathrm{Equation}\left(1\right)\mathrm{is}\mathrm{multiplied}\mathrm{by}10\right]$

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

$$\begin{gathered} \Rightarrow 10\mathrm{x}-\mathrm{x}=24.444....-2.444..... \\ \Rightarrow 9\mathrm{x}=22.0 \\ \Rightarrow \mathrm{x}=\frac{\mathbf{22}}{\mathbf{9}} \end{gathered}$$

Final answer: Hence, the $\frac{p}{q}$ from of the given decimal number is$\frac{\mathbf{22}}{\mathbf{9}}$.