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Maths Query > Unit > Arithmetic > Number System

# Rational Numbers with Number Line Representation

Found in topics: Numbers

## Introduction

To start with what are rational numbers and how do we write them, there is a brief introduction about them in the chapter Types of Number Natural, Whole, Integer, Real Rational.
We will discuss more about them here and learn if we can represent them on the number line and how.

## What is rational number?

A number which can be written in the form of $\frac{\text{p}}{\text{q}}$ , where p and q are integers and q ≠ 0.

Example

$\frac{1}{2}$ , $\frac{6}{7}$ , $\frac{9}{10}$ , $\frac{3}{10}$ etc.

Note

Even 0 is also a rational number as 0 can be written as $0=\frac{0}{1}$

## How to represent rational number on number line.

Rational numbers can be written on the same number line as usual numbers.
The following steps will help in representing a rational number on the number line.

Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Divide distance between 0 and 1 into n equal points.
Mark the points as $\frac{1}{\text{n}}$ , $\frac{2}{\text{n}}$ , $\frac{3}{\text{n}}$ , $\frac{4/mn>\text{n}}{}$ etc.

Let’s learn the above steps with an example.

Example

Example 1: Represent $\frac{3}{7}$ on number line.
Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Here, n = 7.
So, divide distance between 0 and 1 into 7 equal points.
Length of each part between two adjacent points is $\frac{1}{7}$ .
Now, start from 0 and mark the point $\frac{3}{7}$ on the number line.
So, OA = $\frac{3}{7}$

Example 2: Represent $\frac{7}{4}$ on number line when value of denominator is less than value of numerator.
Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Here, n = 4.
So, divide distance between 0 and 1 into 4 equal points and do the same from 1 to 2, i.e. divide them into 4 equal parts.
Length of each part between two adjacent points is $\frac{1}{4}$ .
Mark the point $\frac{7}{4}$ on the number line.
So, OA represents $\frac{7}{4}$

## Draw a number line and represent the following rational numbers on the number line.

1. $\frac{5}{4}$
2. $\frac{4}{5}$
3. $\frac{3}{2}$
4. $\frac{2}{7}$
5. $\frac{2}{3}$
Last updated on: 27-08-2024