Introduction

Natural Numbers:

1. Non-negative counting numbers excluding zero are called Natural Numbers.

2. It is denoted as N = 1, 2, 3, 4, 5, ……….

Whole Numbers:

1. All-natural numbers including zero are called Whole Numbers.

2. It is denoted as W = 0, 1, 2, 3, 4, 5, …………….

Integers:

1. All-natural numbers, negative numbers and 0, together are called Integers.

2. It is denoted as Z = – 3, – 2, – 1, 0, 1, 2, 3, 4, …………..

Rational Numbers:

1. The number ‘a’ is called Rational if it can be written in the form of r/s where ‘r’ and ‘s’ are integers and s ≠ 0, Q = 2/3, 3/5, etc. all are rational numbers.

To find the rational number between two given numbers ‘a’ and ‘b’ is  (a+b)/2

Example:

Find 2 rational numbers between 4 and 5.

Sol: To find the rational number between 4 and 5  (a+b)/2 = (4+5)/2 = 9/2

To find another number we will follow the same process again.

(1/2) (4 + (9/2)) = (1/2) (17/2) = 17/4

Irrational Numbers:

The number ‘a’ which cannot be written in the form of p/q is called irrational, where p and q are integers and q ≠ 0 or you can say that the numbers which are not rational are called Irrational Numbers.

Example - √7, √11, etc.

Real Numbers:

1. All numbers including both rational and irrational numbers are called Real Numbers.

2. It is denoted as R = – 2, – (2/3), 0, 3 and √2