Express the following as a fraction in simplest form: 0.365 - Vidyadip

Question

Express the following as a fraction in simplest form:
$0.\overline{365}$

✓

Answer

Let $\text{x}=0.\overline{365}$
$\therefore\text{x}=0.3656565\dots(1)$
$\text{10x}=3.656565\dots(2)$
$\text{1000x}=365.656565\dots(3)$
On subtracting equation (2) from (3), we get
$\text{990x}=362$
$\Rightarrow\text{x}=\frac{362}{990}$
$=\frac{181}{495}$
Hence, $0.365=\frac{\overline{181}}{495}$

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