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Two types of decimal

Once we have defined Set 3 (the rational numbers), we can define two distinct types of decimals:

Terminating decimals: those which 'stop' at a given number of decimal places, for example 0.5 (1 decimal place), 0.75 (2 decimal places), 3.125 (3 decimal places) and so on.

Recurring decimals: those which do not 'stop' at a given number of decimal places but which may have a repeating digit or repeating set of digits after the decimal point, for example:

All rational numbers ('fractions') when represented as decimals will either terminate or recur.