September 26, 2023

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# What are the Different Types of Numbers? In Mathematics, the numbers system represents numbers on the number line with the help of symbols and rules. It helps to perform various mathematical operations ranging from simple arithmetic operations to the most significant scientific calculations. Before discussing the different types of numbers, we will look at the brief explanation on the number line.

A number line is used to represent the numbers on the straight line using the fixed interval. We can represent various types of numbers like natural numbers, whole numbers, rational numbers, and integers in the number line. The numbers on the number line will increase from left to right or we can say that the number decreases while moving from right to left. In the number line, the number 0 is the origin. The negative numbers are represented on the left side of the origin, and the positive numbers are represented on the right side of the origin.

## What are Numbers?

The mathematical symbols that range from 0-9 are called digits. The value created by the combination of digits is called a number. For example, 82 is a number, which is the combination of digits 8 and 2. The numbers can be positive or negative, even or odd numbers. Now, let us discuss different types of numbers in detail.

### Natural Numbers

Natural numbers are called counting numbers that range from 1 to infinity and are represented using the letter “N”. Natural numbers are also known as counting numbers. The set of natural numbers is given as N = {1, 2, 3,..}.

### Whole Numbers

The whole numbers are generally natural numbers, but it includes zero also. The notation used to represent whole numbers is “W”. The set of whole numbers is given as W = {0, 1, 2, ….}.

### Integers

Integers are the set of whole numbers and the negative representation of natural numbers. In other words, the integers are the collection of natural numbers and negative forms of natural numbers and zero. The integers are represented using the notation “Z”, and the set notation of integers is given as Z = {…., -3, -2, -1, 0, 1, 2, 3, …}.

### Rational Numbers

Rational numbers are one of the types of numbers which can be expressed in the form of p/q. Here, p and q represent integers, and q is not equal to 0.

Note: Fractions are the numbers that are written in the form of a/b, where the upper part of the fraction is called the numerator, and the lower part of the fraction is called the denominator.

For example, ¾, ⅖, etc., are rational numbers.

### Irrational Numbers

The numbers which cannot be expressed in the form of p/q are called irrational numbers. Few examples of irrational numbers are √2, √5, π and so on.

### Real and Imaginary Numbers

The combination of real and imaginary numbers are called complex numbers, and their standard form is a+bi, where a and b are the real number part, and “i” is called an imaginary number. Real numbers are numbers that include whole numbers, fractions, integers, etc. But imaginary numbers are numbers that are not real numbers. The imaginary numbers are the numbers that result in the square root of negative numbers and have no definite values. examples of complex numbers include 2+5i, 1+4i, etc.

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