## Types of number or Number system

In mathematics, we classify number in different categories. This classification of number is known as number system or types of numbers. The following chart shows the classification of number.

## Natural Number

Natural numbers are also known as counting numbers. Natural numbers starts from 1. The number series include 1, 2, 3, ... and so on. It does not include any negative number or '0'. These are the number which we use to count things, like number of animals, number of trees, etc.

## Whole Number

If we include the number '0' to the system of natural number, the new set which we get is set of whole number. The first number of whole number series is 0.

## Integers

Integers are the set of whole numbers plus negative numbers. Numbers less than zero are known as negative numbers. The number series includes

..., –3, –2, –1, 0, 1, 2, 3, ...

## Rational numbers

Rational numbers are the numbers of the form $\frac{p}{q}$ where p and q are integers and q ≠ 0. These are of two types:

### 1. Non terminating, repeating numbers

In this type, if we write the rational number (in the form of $\frac{p}{q}$) in decimal form, the decimal part (a set of few numbers) start repeating itself after certain digits. For example,

a) $\frac{4}{3}$ = 1.33333...

b) $\frac{523}{33}$ = 15.848484...

We can see that the decimal part will never end i.e, it is non terminating, but it repeats after some. Such numbers are know as non - terminating, repeating numbers.

### 2. Terminating numbers

In this type, if we write the rational number in decimal form, we will get a particular number and the decimal parts terminate. There is no repeating unit. For example,

a) $\frac{13}{2}$ = 6.5

b) $\frac{245}{4}$ = 61.25

Therefore, set of rational numbers contain set of integers plus the decimal numbers (non terminating, repeating and terminating).

## Irrational Number

Non terminating, non repeating numbers are know as Irrational numbers. They can not be expressed in he form of $\frac{p}{q}$ where p, q are integers. examples of irrational numbers are:

a) $\sqrt2$ = 1.412135623709548801..

b) $\sqrt3$ = 1.732050807568877293..

We can see that the decimal forms never terminates and it does not take any specific pattern i.e., it does not repeat. Such numbers are known as irrational numbers.

## Real Numbers

The set of rational numbers plus set of irrational numbers are known as real numbers. All the points on a number line represent a specific real number.

## Imaginary number

These numbers are based on the imaginary concept of number ' i ', which is defined as:

**i ^{2} = -1**

Any real number followed by ' i ' is known as imaginary number. example: 2i, 3i, –21i, etc..

## Complex number

Complex number is a combination of a real number and an imaginary number. These are expressed as:

General form: a + bi

where, a = real part

b = imaginary part

Example :

a) 4 + 3i

4 is real and 3i is imaginary

b) 3 – 6i

3 is real and -6i is imaginary

The diagram below shows the way one number type is contained in (subset of) another number type.