# How to represent rational and irrational numbers in a number line ?

Rational numbers in number line :

To represent a positive rational number on the number line, follow the below steps:

In order to represent a fraction on the number line, we need to divide the line segment between two whole numbers into 'n' equal parts where n represents the denominator of the fraction.

Therefore,

If we have to represent the fraction $\frac{1}{5}$ on the number line, we need to divide the line segment between 0 and 1 into five equal parts.

In the above figure, point A represents the fraction $\frac{1}{5}$.

To represent negative rational numbers, follow the below steps:

For example,

To represent $\frac{-2}{6}$ on the number line,

1) Draw a number line.

2) As the number $\frac{-2}{6}$ is a negative number so it will be on the left of zero. The number$\frac{-2}{6}$ lies between 0 and $-1$

3) Divide the line segment between 0 and $-1$ into 6 parts(6 is the denominator here).

4) Move two parts to the left of 0 (2 is the numerator here).

5) Therefore, A is the required point.

Representation of irrational numbers in number line :

To represent an irrational number, we should use Pythagoras theorem

Hypotenuse2=Base2+Height2 Hypotenuse^{2}= Base^{2}+ Height^{2}" role="presentation" style="display: inline; line-height: normal; font-size: 16.94px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">$Hypotenuse^{2}= Base^{2}+ Height^{2}$

• Now first draw a number line and mark '0' , '1' and '2'
• With 1 units as length draw a line from '2'  such that it is perpendicular to the line.
• Now join the point (0) and the end of new line of 1 unit length.
• A right angled triangle is constructed.
• Now let us name the triangle as ABC such that BC is the height (perpendicular), AB is the base of triangle and AC is the hypotenuse of the right angled triangle ABC.

You know AC2=22+12 A C^{2}=2^{2}+1^{2} " role="presentation" style="display: inline-table; line-height: normal; font-size: 16.94px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;"> A C^{2}=2^{2}+1^{2}" role="presentation" style="color: rgb(204, 0, 0); font-style: italic; transition: none 0s ease 0s; display: inline; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; line-height: normal;">$A C^{2}=2^{2}+1^{2}$

AC2=4+1 A C^{2}=4+1" role="presentation" style="display: inline-table; line-height: normal; font-size: 16.94px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;"> A C^{2}=4+1" role="presentation" style="color: rgb(204, 0, 0); font-style: italic; transition: none 0s ease 0s; display: inline; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; line-height: normal;">$A C^{2}=4+1$
AC2=5 A C^{2}=5 " role="presentation" style="display: inline-table; line-height: normal; font-size: 16.94px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;"> A C^{2}=5" role="presentation" style="color: rgb(204, 0, 0); font-style: italic; transition: none 0s ease 0s; display: inline; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; line-height: normal;">$A C^{2}=5$

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Updated on: 10-Oct-2022

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