Express the following decimals in the form p q : 125.3 - Vidyadip

Question

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $125.\bar{3}$

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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, $\text{x}=\frac{376}{3}$

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