Express the following decimals in the form p q : 0.54 - Vidyadip

Question

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $0.\overline{54}$

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Answer

Let $\text{x}=0.\overline{54}$
$\Rightarrow\text{x}=0.5454\ ...(\text{i})$ Multiplying equation $(i)$ by $100$,
We get, $100\text{x}=54.5454\ ...(\text{ii}) $ Subtracting equation $(i)$ by equation $(ii)$
$\therefore\ 100\text{x}-\text{x}=54$
$\Rightarrow99\text{x}=54$
$\Rightarrow\text{x}=\frac{54}{99}=\frac{6}{11}$
Hence, $0.\overline{54}=\frac{6}{11}$

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