Types of Numbers

Numbers play a vital role in our lives, such as counting things, time, money, age and much more. The ten mathematical digits (0 to 9) are used to represent all of these quantities. In this article, we will be discussing the different types of numbers in mathematics with examples.

Different Types of Numbers

Following are the main types of numbers used in school mathematics.

Natural Numbers

Numbers start from 1 and up. NO Zero, NO numbers with decimals, and NO Negative numbers are in this group.

Natural numbers are also called counting numbers or positive integers because these numbers are used for counting and ordering.

The set of natural numbers is denoted by the letter ‘N’.

N = {1, 2, 3, 4, 5, ….}
Examples: 45, 109, 59, 12, etc.


Whole Numbers

Whole Numbers are simply the natural numbers, including zero (i.e., natural numbers + 0).

NO numbers with decimals and NO Negative numbers are in this group.

The set of whole numbers is denoted by W.

W = {0, 1, 2, 3, 4, 5, ….}
Examples: 45, 0, 59, 11, 110 etc.



Integers are all whole numbers and their negatives. The set of integers are denoted by Z.

Z = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Examples: -45, 0, 59, -11, 110 etc.


Rational Numbers

Any number written in the form of fraction or ratio, i.e., a/b, where a and b are integers. [Tip to remember: root word of rational is ‘ratio’].

The letter ‘Q’ denotes a rational number.

[Note: The denominator cannot be 0, but the numerator can be].

Examples: 1/4, 2/5, 7/2, ⁻4/3, 0/1 etc.


Irrational Numbers

A number that cannot be written in the form of a fraction or ratio. Irrational Numbers may be endless (never terminating) non-repeating decimals.

The letter ‘ P denotes an irrational number.’
Examples: 𝜋=3.14159…,  √3=1.73205, Euler’s constant, etc.


Real Numbers

All the numbers that can be found on a number line. It can be natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Irrational numbers are real numbers, but not all real numbers are irrational numbers. A real number is denoted by the letter ‘R.’

Examples: 7, ¾, 0.333, √2, 0, -19, 20, 𝜋 etc.

>> Prime and Composite Numbers



Classify each number in as many categories as possible.

(1) -25

(2) 0

(3) 1/5

(4) 1

(5) √2

(6) -16/4

(7) 3.1428571428571….


1 . Integer, rational, real
2 . Whole, Integer, rational, and real
3 . Rational, real
4 . Natural, whole, Integer, rational, real
5 . Irrational, real
6 . Integer, rational, real (because -16/4 can be rewritten as -4)
7 . Irrational, real

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