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Write the recurring decimal 0,52 as a fraction

June 3, 2026Mathematics

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Answer

\frac{52}{99}

4 steps

Let $x$ be the recurring decimal.
$x = 0.\overline{52}$
This means $x = 0.525252...$
Multiply the equation by 100 since there are two repeating digits.
$100x = 52.525252...$
Subtract the original equation ( $x = 0.525252...$ ) from the new equation ( $100x = 52.525252...$ ).
$100x - x = 52.525252... - 0.525252...$ $99x = 52$
Solve for $x$ by dividing both sides by 99.
$x = \frac{52}{99}$
The fraction cannot be simplified further.

The recurring decimal $0.\overline{52}$ as a fraction is $\boxed{\frac{52}{99}}$ .

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