Question
Express the following as a fraction in simplest form:
$0.1\bar2$
$0.1\bar2$
✓
Answer
Let $\text{x}=0.1\bar2$
$\therefore\text{x}=0.1222\dots(1)$
$\text{10x}=12.222\dots(2)$
On subtracting equation (1) from (2), we get
$\text{9x}=12$
$\Rightarrow\text{x}=\frac{12}{9}$
$\therefore0.12=\frac{\overline{12}}{9}$
$\therefore\text{x}=0.1222\dots(1)$
$\text{10x}=12.222\dots(2)$
On subtracting equation (1) from (2), we get
$\text{9x}=12$
$\Rightarrow\text{x}=\frac{12}{9}$
$\therefore0.12=\frac{\overline{12}}{9}$
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