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Rational Number and its Representation on Number Line

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 with Examples.
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 pq, where p and q are integers and q ≠ 0.

Example

12, 67, 910, 310 etc.

Note

Even 0 is also a rational number as 0 can be written as 0 = 01

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 1n, 2n, 3n, 4/mn>n etc.

Let’s learn the above steps with an example.

Example

Example 1: Represent 37 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. Example 1. Number line.
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 17.
Now, start from 0 and mark the point 37 on the number line. Example 1. Rational numbers on the number line.
So, OA = 37

Example 2: Represent 74 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. Example 2. Number line
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 14.
Mark the point 74 on the number line. Example 2. Rational numbers on the number line.
So, OA represents 74