Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
$0.\bar{4}$
$0.\bar{4}$
✓
Answer
Let
$\text{x}=0.\bar4$
Now,
$\text{x}=0.\bar4=0.444\ ...(\text{i})$
Multiplying both sides of equation (i) by 10, we get,
$10\text{x}=4.444\ ...(\text{ii}) $
Subtracting equation (i) by (ii)
$\therefore\ 10\text{x}-\text{x}=4.444\ ...-\ 0.444\ ...$
$\Rightarrow9\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar{4}=\frac{4}{9}$
$\text{x}=0.\bar4$
Now,
$\text{x}=0.\bar4=0.444\ ...(\text{i})$
Multiplying both sides of equation (i) by 10, we get,
$10\text{x}=4.444\ ...(\text{ii}) $
Subtracting equation (i) by (ii)
$\therefore\ 10\text{x}-\text{x}=4.444\ ...-\ 0.444\ ...$
$\Rightarrow9\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar{4}=\frac{4}{9}$
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