Expressing Complex Recurring Decimals as Simplest Fractions

Expressing Complex Recurring Decimals as Simplest Fractions

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. \(1.\dot{4}\dot{5}\)
  2. \(0.\overline{045}\)
  3. \(3.2\dot{3}\dot{5}\)
  4. \(0.\overline{1234}\)

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Answer:(a) \(\frac{16}{11}\) (b) \(\frac{5}{111}\) (c) \(\frac{3203}{990}\) (d) \(\frac{1234}{9999}\)

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