# Integers and rational numbers

Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4…

Integers include all whole numbers and their negative counterpart e.g. …-4, -3, -2, -1, 0,1, 2, 3, 4,…

All integers belong to the rational numbers. A rational number is a number

$$\frac{a}{b},\: b\neq 0$$

Where a and b are both integers.

**Example**

The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:

$$\frac{4}{1}$$

Or

$$\frac{8}{2}$$

Or even

$$\frac{-8}{-2}$$

Whereas

$$\frac{1}{5}=0.2$$

is a rational number but not an integer.

A rational number written in a decimal form can either be terminating as in:

$$\frac{1}{5}=0.2$$

Or repeating as in

$$\frac{5}{6}=0.83333...$$

All rational numbers belong to the real numbers.

**Video lesson**

Write as rational numbers