Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
$125.\bar{3}$
$125.\bar{3}$
✓
Answer
Let
$\text{x}=125.\bar{3}$
$\Rightarrow\text{x}=125.33\ ...(\text{i})$
Multiplying equation (i) by 10,
$\therefore100\text{x}=1253.33\ ...(\text{ii})$
Subtracting equation (i) by (ii)
$\therefore\ 10\text{x}-\text{x}=1253.33 \ ... -125.33 \ ...$
$\Rightarrow9\text{x}=1128$
$\Rightarrow\text{x}=\frac{1128}{9}=\frac{376}{3}$
Hence, $\text{x}=\frac{376}{3}$
$\text{x}=125.\bar{3}$
$\Rightarrow\text{x}=125.33\ ...(\text{i})$
Multiplying equation (i) by 10,
$\therefore100\text{x}=1253.33\ ...(\text{ii})$
Subtracting equation (i) by (ii)
$\therefore\ 10\text{x}-\text{x}=1253.33 \ ... -125.33 \ ...$
$\Rightarrow9\text{x}=1128$
$\Rightarrow\text{x}=\frac{1128}{9}=\frac{376}{3}$
Hence, $\text{x}=\frac{376}{3}$
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