Converting Recurring Decimals to Fractions in Simplest Form

Converting Recurring Decimals to Fractions in Simplest Form

IP 1

Express each of the following recurring decimals as a fraction in the form of \(\frac{p}{q}\) in the lowest term, where \(p\) and \(q\) are integers and \(q\ne0\).

  1. \(0.\dot{6}\)
  2. \(0.\dot{8}\dot{1}\)
  3. \(0.\dot{5}\dot{6}\)
  4. \(2.\dot{7}\)

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Answer:(a) \(\frac{2}{3}\) (b) \(\frac{9}{11}\) (c) \(\frac{56}{99}\) (d) \(\frac{25}{9}\)

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