## 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.

**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.

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 number line.

So, OA represents \(\frac{7}{4}\)