Question

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

(iv) $0.1\overline{2}$

Answer 1

Solution:

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

$$\begin{gathered} \mathrm{Let}\mathrm{x}=0.1\overline{2}=0.12222...........\left(1\right) \\ \Rightarrow 10x=1.2222..............\left(2\right)[\mathrm{Multiply}\mathrm{equation}(1)\mathrm{by}10] \\ \Rightarrow 100x=12.2222...........\left(3\right)[\mathrm{Multiply}\mathrm{equation}(1)\mathrm{by}100] \end{gathered}$$

Subtract equation (2) from equation (3),

$$\begin{gathered} \Rightarrow 90x=11 \\ \Rightarrow x=\frac{11}{90} \end{gathered}$$

Final answer: Hence, the $\frac{p}{q}$ form of the given decimal expression is $\frac{\mathbf{11}}{\mathbf{90}}$.