Question
Express the following as a fraction in simplest form:
$2.2\bar4$
$2.2\bar4$
✓
Answer
Let $\text{x}=2.2\bar4$
$\therefore\text{x}=2.2444\dots(1)$
$\text{10x}=22.2444\dots(2)$
$\text{100x}=224.444\dots(3)$
On subtracting equation (2) from (3), we get
$\text{90x}=202$
$\Rightarrow\text{x}=\frac{202}{90}$
$=\frac{101}{45}$
Hence, $2.24=\frac{\overline{101}}{45}$
$\therefore\text{x}=2.2444\dots(1)$
$\text{10x}=22.2444\dots(2)$
$\text{100x}=224.444\dots(3)$
On subtracting equation (2) from (3), we get
$\text{90x}=202$
$\Rightarrow\text{x}=\frac{202}{90}$
$=\frac{101}{45}$
Hence, $2.24=\frac{\overline{101}}{45}$
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