Types of Numbers in Math

In Math, numbers can be categorized as specific types of number.

Listed below are the main groups certain types of numbers can fall into.

Types of Numbers

Sometimes known as the counting numbers. The natural numbers are the group of whole numbers larger than zero.

{ 1 , 2 , 3 , 4 , 5 , …………… }

Very similar to the natural numbers, whole numbers are every number larger than zero but also including zero.

{ 0 , 1 , 2 , 3 , 4 , ……………}

Integers are numbers that are positive and negative whole numbers, as well as zero.

{ ……………… , -3 , -2 , -1 , 0 , 1 , 2 , 3 , ……………..}

Quotient numbers, which can also be referred to as rational numbers, are numbers that can be written as a fraction of two integers.

For example

\bf{\frac{1}{2}}

\bf{\frac{3}{2}}

, and even

\bf{\frac{2}{1}}

is a quotient.

Irrational numbers are numbers that can’t be written as an exact fraction/quotient of two integers.

Numbers such as π and √2 are irrational numbers.

Surds are numbers which contain roots and are also irrational numbers.

The numbers

\sqrt{2}

\sqrt{6}

and

5\sqrt[3]{2}

are surds.

They can’t be simplified exactly to a whole number.

The numbers

\sqrt{4}

and

\sqrt{9}

are NOT surds.

As they can be written as a whole number.

\sqrt{4} = 2

\sqrt{9} = 3

Any real number, all of the number types in the previous groups are real numbers, even the irrational numbers.

A prime number is any whole number greater than 1 that can only be divided evenly by 1 and itself.

For example: 3, 11 and 17 are prime numbers.