Convert Repeating Decimal to Fraction

To convert the repeating decimal \(0.\overline{53}\) to a fraction, we can use an algebraic method.

1. Let the given decimal be represented by a variable, say \(x\). \(x = 0.\overline{53}\) This means \(x = 0.535353...\)

2. Identify the repeating block. The repeating block is '53', which has 2 digits.

3. Multiply the equation by \(10^2\) (since there are 2 repeating digits) to shift the decimal point two places to the right. \(100x = 53.\overline{53}\) This means \(100x = 53.535353...\)

4. Subtract the original equation (\(x = 0.\overline{53}\)) from the new equation (\(100x = 53.\overline{53}\)). \(100x - x = 53.\overline{53} - 0.\overline{53}\) \(99x = 53\)

5. Solve for \(x\) by dividing both sides by 99. \(x = \frac{53}{99}\)

Therefore, the value of \(0.\overline{53}\) as a fraction is \(\frac{53}{99}\).