Recurring Decimals and Fractions

Recurring Decimals and Fractions

IP 1

Recurring Decimals

A recurring decimal (or repeating decimal) is a decimal number in which one or more digits repeat infinitely.

It is usually denoted with a dot (or a bar) over the repeating part, e.g., \(0.\dot{3}\) (or \(0.\bar{3}\)), which means \(0.333...\); or \(0.\dot{5}\dot{6}\) (or \(0.\overline{56}\)), which means \(0.565656...\)

Any recurring decimal can be expressed as \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne0\), and thus recurring decimals are rational numbers.

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Answer:Every recurring decimal is rational and can be expressed as \(\frac{p}{q}\), where \(p,q\in\mathbb{Z}\) and \(q\ne0\).

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