# Decimal

The word decimal technically refers to the base-ten number system that we use every day. When most people talk about decimals, however, they are referring to decimal numerals such as 5.24, so on the rest of this page, the word decimal will be used to mean decimal numeral.

A decimal contains the decimal point. Any number on the number line – whether, positive, negative or zero – can be expressed as a decimal. The whole numbers (integers) can be written with zeroes in place value columns after the decimal point. For example, 7 can be written as 7.0, 7.00, 7.000 etc. and -18 can be written as -18.0, -18.00, -18.000 etc. (Note that in the context of rounding, these may mean different things, despite all appearing to refer to the same integer.)

Decimals are most commonly used when dealing with numbers that are not whole numbers. Any fraction is a rational number, and can be written as either a terminating or recurring decimal:

$$\dfrac{3}{4}=0.75$$ is a terminating decimal as its decimal expansion comes to an end.

$$2 \frac{5}{8}=2.625$$ is a terminating decimal as its decimal expansion comes to an end.

$$\dfrac{1}{3}=0.33333… = 0.\dot{3}$$ is a recurrring decimal as its decimal expansion goes on forever but has a clearly repeating pattern.

$$\dfrac{124}{990}=0.0124124124… = 0.0\dot{1}2\dot{4}$$ is a recurring decimal as its decimal expansion goes on forever but has a clearly repeating pattern.

Irrational numbers – such as surds and $$\pi$$ – can’t be expressed exactly as fractions (with integer numerator and denominators). These numbers have decimal expansions which go on forever i.e. they do not terminate and they don’t even have a recurring pattern.

Decimals can also be expressed as percentages.

Relevant lessons: