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
ab,b≠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:
41
or
82
or even
−8−2
Whereas
15=0.2
is a rational number but not an integer.
A rational number written in a decimal form can either be terminating as in:
15=0.2
Or repeating as in
56=0.83333...
All rational numbers belong to the real numbers.
If you look at a numeral line
picture05
You notice that all integers, as well as all rational numbers, are at a specific distance from 0. This distance between a number x and 0 is called a number's absolute value. It is shown with the symbol
|x|
If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. Opposites have the same absolute value since they are both at the same distance from 0.
|10|=10=|−10|