Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$125.\bar{3}$
✓
Answer
Let$\text{x}=4.\bar{7}$
$\Rightarrow\text{x}=4.77\ ...(\text{i})$
Multiplying equation (i) by 10,$\therefore10\text{x}=47.77\ ...(\text{ii})$
Subtracting equation (i) by (ii)$\therefore\ 10\text{x}-\text{x}=47.77 \ ... -4.77 \ ...$
$\Rightarrow9\text{x}=43$
$\Rightarrow\text{x}=\frac{43}{9}$
Hence, $4.\bar{7}=\frac{43}{9}$
$\Rightarrow\text{x}=4.77\ ...(\text{i})$
Multiplying equation (i) by 10,$\therefore10\text{x}=47.77\ ...(\text{ii})$
Subtracting equation (i) by (ii)$\therefore\ 10\text{x}-\text{x}=47.77 \ ... -4.77 \ ...$
$\Rightarrow9\text{x}=43$
$\Rightarrow\text{x}=\frac{43}{9}$
Hence, $4.\bar{7}=\frac{43}{9}$
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