Periodic and non-periodic fractions

A decimal expansion is called periodic (or repeating) if, after some point, a finite sequence of digits repeats indefinitely. If no such repeating sequence exists, the decimal is non-periodic (or non-repeating).

Important properties

• Every rational number (fraction of integers) has a decimal expansion that either terminates or becomes periodic.

• Non-periodic, non-terminating decimals represent irrational numbers.

• Terminating decimals can be seen as periodic with the repeating part being 0.