Types of Numbers in Maths

Numbers are the foundation of mathematics. They help us count, measure, calculate, and solve problems in everyday life.

This blog will guide you through the different types of numbers in maths with definitions, properties, and examples. By the end, you’ll understand how each type of number works and why they are important.

Let’s begin with the basics and then explore all types step by step.

What Are Numbers in Maths?

Numbers are symbols used to represent quantities. They allow us to perform operations such as addition, subtraction, multiplication, and division.

In mathematics, numbers are classified into different types based on their properties and use.

Types of Numbers in Maths

Here is a complete list of the different types of numbers in maths:

• Natural Numbers
• Whole Numbers
• Integers
• Rational Numbers
• Irrational Numbers
• Real Numbers
• Complex Numbers
• Prime Numbers
• Composite Numbers

Natural Numbers

Natural numbers are the numbers we use for counting.

• Represented by N = {1, 2, 3, 4, …}
• Do not include 0 or negative numbers.

Example: 1, 2, 3, 100

Learn more about What are Natural Numbers? Properties & Examples

Whole Numbers

Whole numbers include all natural numbers and 0.

• Represented by W = {0, 1, 2, 3, …}
• They do not include negatives or fractions.

Example: 0, 5, 12, 200

Learn more about What is Whole Number? Definition, Properties & Examples

Integers

Integers include positive numbers, negative numbers, and zero.

• Represented by Z = {… −3, −2, −1, 0, 1, 2, 3 …}
• Do not include fractions or decimals.

Example: −7, −1, 0, 4, 10

Learn more about What are Integers? Properties & Rules of Integers

Rational Numbers

Rational numbers can be written as p/q, where p and q are integers and q ≠ 0.

• Includes fractions and terminating/repeating decimals.
• Represented by Q.

Example: 1/2, −3/4, 0.75, 7

Learn more about What are rational Numbers? Properties & Examples

Irrational Numbers

Irrational numbers cannot be written as fractions. Their decimals are non-terminating and non-repeating.

Example: √2, π, e

Learn more about What are Irrational Numbers? Properties & Examples

Real Numbers

Real numbers include both rational and irrational numbers.

They can be placed on a number line.

Example: −2, 0, 3/4, √5, π

Learn more about What Are Real Numbers? Properties & Examples

Complex Numbers

Complex numbers include a real part and an imaginary part.

• Form: a + bi where i = √(−1).

Example: 3 + 2i, −5 + i

Learn more about What Are Complex Numbers? Properties & Operations

Prime Numbers

Prime numbers are natural numbers greater than 1 that have only two factors: 1 and themselves.

Example: 2, 3, 5, 7, 11

Learn more about What Are Prime Numbers? properties & 1 To 1000 Prime Numbers

Composite Numbers

Composite numbers are numbers with more than two factors.

Example: 4 (factors: 1, 2, 4), 6, 9, 12

Learn more about What Are Composite Numbers? Types and Properties

Even Numbers

Even numbers are divisible by 2.

Example: −4, 0, 8, 100

Odd Numbers

Odd numbers are not divisible by 2.

Example: −3, 1, 5, 11

Properties of Numbers

Numbers follow certain properties that make calculations easier:

• Closure Property: Addition and multiplication of two real numbers always give another real number.
• Commutative Property: a + b = b + a, a × b = b × a
• Associative Property: (a + b) + c = a + (b + c)
• Distributive Property: a × (b + c) = ab + ac

Chart of Number System

Here’s a simple breakdown:

• Real Numbers
  • Rational Numbers
    • Integers
      • Whole Numbers
        • Natural Numbers
  • Irrational Numbers
• Complex Numbers

Examples of Different Types of Numbers

• Natural: 5, 9
• Whole: 0, 10
• Integer: −7, 0, 12
• Rational: 2/3, 0.5
• Irrational: √2, π
• Real: −3, 2.5, √5
• Complex: 4 + i
• Prime: 13
• Composite: 15
• Even: 20
• Odd: 21

Conclusion

Numbers are the foundation of mathematics. From natural and whole numbers to complex numbers, each type plays a unique role.

Prime and composite numbers help in factorization, while rational and irrational numbers explain decimals and fractions.

Real and complex numbers extend mathematics into advanced areas. Understanding these types of numbers strengthens your maths skills and helps you solve problems in both academics and daily life.

FAQs

Q1. What are natural numbers?
Natural numbers are counting numbers starting from 1.

Q2. Is zero a whole number?
Yes, zero is the first whole number.

Q3. Are integers rational numbers?
Yes, every integer can be written as p/q.

Q4. Is π a rational number?
No, π is an irrational number.

Q5. What is the only even prime number?
2 is the only even prime.

Q6. What is the smallest composite number?
The smallest composite number is 4.

Q7. Are all real numbers rational?
No, some real numbers are irrational.

Q8. What is a complex number?
A complex number has a real and an imaginary part.

Q9. Are negative numbers integers?
Yes, integers include both positive and negative numbers.

Q10. Why are numbers important in maths?
They form the basis of all calculations and problem-solving.