Convert Repeating Decimal to Fraction
To convert the repeating decimal \(0.\overline{53}\) to a fraction, we can use an algebraic method.
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Let the given decimal be represented by a variable, say \(x\). \(x = 0.\overline{53}\) This means \(x = 0.535353...\)
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Identify the repeating block. The repeating block is '53', which has 2 digits.
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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 \(100x = 53.535353...\)
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Subtract the original equation (\(x = 0.\overline{53}\)) from the new equation (\(100x = 53.\overline{53}\)). \(100x - x = 53.\overline{53} - 0.\overline{53}\) \(99x = 53\)
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Solve for \(x\) by dividing both sides by 99. \(x = \frac{53}{99}\)
Therefore, the value of \(0.\overline{53}\) as a fraction is \(\frac{53}{99}\).
Similar Questions
The correct expression of 6.4646464646.... in the fractional form is:
Important Questions from Decimals
What is the result when 0.129129129… is converted to a fraction?
Which of the following statement(s) is/are correct?
I. (3/11) > 0.3
II. (7/8) > 0.86
The value of \(1.\overline{3}+0.\overline{69}-0.5\overline{23}\) is equal to:
The value of \(0.\bar 4 + 0.5 \bar 9 - 0.4 \overline{23}\) is equal to:
If 19 × 23 = 437, then find the value of (190 × 0.023).
