## 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
$\frac{\text{p}}{\text{q}}$,
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
$\frac{1}{\text{n}}$,
$\frac{2}{\text{n}}$,
$\frac{3}{\text{n}}$,
$\frac{\mathrm{4/mn>\text{n}}}{}$
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
$\frac{7}{4}$