Numbers are strings of digits used to indicate magnitude. They measure size - how big or small a quantity is. In mathematics there are several types of numbers, but they fall into two main classes, the counting numbers, and scalars.

Counting numbers, Natural Numbers

These are used to count the number of objects. They are positive whole numbers and have no fractional parts. For example 12 cars, 45 students, 3 houses. For more on this see Counting numbers and Natural numbers.


These are numbers used to measure some quantity to any desired degree of accuracy. For example a building height is 12.388 meters, or speed of an aircraft is 810.31 kilometers per hour. They can have decimal places or fractional parts. See also Scalar definition. Within this category there are several types of number:

Number notation

There are various ways that numbers can be written or diagrammed.

Some numbers are not numbers at all

Sometimes numbers are used as identifiers. Instead of measuring how big something is or counting things, they are used to label objects in the real world. For example, a student ID number is not used to measure anything. It is simply a string of digits that identifies one particular student.

It makes no sense to try and do arithmetic with them. Dividing a student number by two or finding the square root of a phone number has no meaning.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values