Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
$0.\overline{621}$
$0.\overline{621}$
✓
Answer
Let
$\text{x}=0.\overline{621}$
Now, $\text{x}=0.621621\ ...(\text{i})$
Multiplying equation (i) by 1000,
$\therefore1000\text{x}=621.621621\ ...(\text{ii})$
Subtracting equation (i) by (ii)
$\therefore\ 1000\text{x}-\text{x}=621$
$\Rightarrow999\text{x}=621$
$\Rightarrow\text{x}=\frac{621}{999}=\frac{69}{111}=\frac{23}{37}$
Hence, $0.\overline{621}=\frac{23}{37}$
$\text{x}=0.\overline{621}$
Now, $\text{x}=0.621621\ ...(\text{i})$
Multiplying equation (i) by 1000,
$\therefore1000\text{x}=621.621621\ ...(\text{ii})$
Subtracting equation (i) by (ii)
$\therefore\ 1000\text{x}-\text{x}=621$
$\Rightarrow999\text{x}=621$
$\Rightarrow\text{x}=\frac{621}{999}=\frac{69}{111}=\frac{23}{37}$
Hence, $0.\overline{621}=\frac{23}{37}$
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