What is a recurring decimal?

A recurring decimal is a decimal number in which a digit or group of digits repeats infinitely.

In mathematics, a recurring decimal is a way of representing a number that cannot be expressed as a finite decimal. For example, the fraction 1/3 is equal to 0.333..., where the digit '3' repeats indefinitely. This is often written as \(0.\overline{3}\) to indicate that the '3' is recurring. Similarly, the fraction 2/7 is equal to 0.285714285714..., where the sequence '285714' repeats infinitely, and can be written as \(0.\overline{285714}\).

Recurring decimals can be identified by performing long division. When you divide the numerator by the denominator, if you notice that the same remainder starts to appear, it means the digits will start repeating. For instance, dividing 1 by 7 gives 0.142857142857..., where '142857' is the repeating sequence.

It's important to distinguish between terminating and recurring decimals. A terminating decimal has a finite number of digits after the decimal point, such as 0.5 or 0.75. In contrast, a recurring decimal never ends but instead has a repeating pattern.

Understanding recurring decimals is crucial for GCSE Maths as it helps in recognising patterns and converting between fractions and decimals. It also lays the groundwork for more advanced topics in mathematics, such as sequences and series. Remember, any fraction where the denominator is not a factor of 10 will either be a terminating or a recurring decimal.