Definition of repeating decimal and examples

A repeating decimal, also called recurring decimal, is a decimal number in which a digit or a set of digits repeats infinitely or without end.

For example, the decimal number 6.333333333  is a repeating decimal.

6.333333333 has only 1 digit that repeats infinitely and that digit is 3.

The decimal number 0.2525252525 has a set of two digits that repeats without end and the set is 25.

The decimal number 4.316316316316 has a set of three digits that repeats without end and the set is 316.

When writing a repeating decimal, a bar is usually placed over the repeating portion.

For example, you could write

6.333333333 as 6.3

0.2525252525 as 0.25

4.316316316316 as 4.316

More examples of repeating decimals

Can you identify the repeating digit(s) for the following repeating decimals?

1) 0.071071071071

2) 45.4785478547854785

3) 0.068068068068

4) 12.701257012570125

5) 0.5001500150015001

Recognizing a repeating decimal can be tricky as you may have noticed with the five examples above.

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