Types of numbers

In a nutshell

Numbers are used to represent quantities of items, and different types of numbers belong to different sets. For example, integers can be used for counting while rational numbers are better used to describe how much of a portion remains.

Identifying types of numbers

Example 1

What type of number is $$8.6$$?

 $$8.6 = \dfrac{86}{10} = \dfrac{43}{5}$$

Hence as this is the simplest form and both the numerator and denominator are integers, $$8.6$$ is a rational number.

Subsets of numbers

Some of the definitions of numbers overlap. For instance, $$6$$ falls into the category of a natural number, integer, rational number and also a real number. This gives a subset order for the types of numbers which can be seen below:

From the Venn diagram you can see that all natural numbers are integers, all integers are rational numbers, and all rational and irrational numbers are real.