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.