Terminating decimal expansions

Terminating decimals are the numbers that have a fixed or a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole, just like fractions.

Definition

The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. Decimals are used to express the whole number and fraction together that is separated from each other by inserting a "." i.e. a decimal point. For example, 10.4, 10 is the whole number and 4 is the decimal fraction. There are different categories of decimals depending on what type of digits occur after the decimal point, they are:

• Terminating decimal expansion
• Non-terminating recurring decimal expansion
• Non-terminating non-recurring decimal expansion

A number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. The fraction ${\frac {1}{2}}$ has the decimal expansion of 0.5, which is a terminating decimal expansion because digits after the decimal point end after one digit.

Terminating decimals are rational numbers.