Introduction

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

N = 1, 2, 3, 4, 5, ……….

Whole Numbers

All natural numbers including zero are called Whole Numbers.

W = 0, 1, 2, 3, 4, 5, …………

Integers

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

Z = – 3, – 2, – 1, 0, 1, 2, 3, 4, ………

Rational Numbers

The number ‘a’ is called Rational if it can be written in the form of r/s where ‘r’ and ‘s’ are integers and \mathrm{s\ne0},\dfrac{2}{3},\dfrac{3}{5}, etc. all are rational numbers.

How to find a rational number between two given numbers?

To find the rational number between two given numbers ‘a’ and ‘b’.

\mathrm{\dfrac{a+b}{2}}

Example:

Find 2 rational numbers between 4 and 5.

Solution:

To find the rational number between 4 and 5

\mathrm{\dfrac{a+b}{2}=\dfrac{4+5}{2}=\dfrac{9}{2}}

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

\dfrac{1}{2}\left(4+\dfrac{9}{2}\right)=\left(\dfrac{1}{2}\right)\dfrac{17}{2}=\dfrac{17}{4}

Hence the two rational numbers between 4 and 5 are \dfrac{9}{2} and \dfrac{17}{4} .

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