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Rational Number and its Representation on Number Line

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Introduction

To start with what are rational numbers and how do we write them, there is a brief introduction about them here.
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 \(\frac{p}{q}\), where p and q are integers and \(q \; \neq \; 0\).

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 number can be written on number line same as usual numbers.
The following steps will help in representing a rational number 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
Divide distance between 0 and 1 into n equal points.
Mark the points as \(\frac{1}{n}\), \(\frac{2}{n}\), \(\frac{3}{n}\), \(\frac{4}{n}\) 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. 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 \(\frac{1}{7}\).
Now, start from 0 and mark the point \(\frac{3}{7}\) on number line. Example 1. Rational numbers on 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. 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 \(\frac{1}{4}\).
Mark the point \(\frac{7}{4}\) on number line. Example 2. Rational numbers on number line.
So, OA represents \(\frac{7}{4}\)