# Standard form of Rational number

In this chapter we will learn the standard form of rational number along with different methods to convert the given numbers in standard form.

To understand the chapter fully, I will strongly urge to clear the basics of rational number by clicking the red link.

## Define rational number in standard form

We know that rational number are represented in the form of \mathtt{\ \frac{a}{b}} .

Where a & b are integers.

Also number ” a ” is called numerator and ” b” is called denominator.

In standard form, the rational number is expressed in such a manner that there is no common factor left between numerator and denominator (apart from number 1 ).

In other words, to get the rational number in ” standard form “, we have the reduce the fraction to its lowest terms so that no common factor is left between numerator and denominator.

For example;
Let the given rational number is \mathtt{\frac{6}{42}}

Explanation
Note that number 6 is common factor between numerator and denominator.

So divide the fraction by 6 in both upper and lower part.

\mathtt{\Longrightarrow \frac{6}{42}}\\\ \\ \mathtt{\Longrightarrow \ \frac{6\div 6}{42\div 6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{7}}

Now there is no common factor between numerator and denominator.

Hence, the number is reduced to standard form with value \mathtt{\ \frac{1}{7}}

## How to reduce rational number to standard form ?

Given below are steps to reduce the given rational number to its standard form.

(i) Represent the rational number in form of fraction

(ii) Find the HCF of numerator and denominator

(iii) Divide both numerator & denominator by HCF value and you will get the standard form.

I hope the above process is clear, let us solve some examples for better clarity.

Example 01
Find the standard form of \mathtt{\frac{15}{6}}

Solution
Do the following steps;

(i) Take HCF of numerator and denominator.

HCF ( 15, 6 ) = 3

It tells that 3 is the common factor between numerator and denominator.

(ii) Now divide numerator & denominator by 3

\mathtt{\Longrightarrow \frac{15}{6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{15\div 3}{6\div 3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{2}}

Hence, \mathtt{\frac{5}{2}} is the standard form of given fraction.

Example 02
Find the standard form of rational number \mathtt{\frac{18}{12}}

Solution

(a) Find HCF of numerator and denominator.

HCF ( 18, 12 ) = 6

(b) Now divide numerator and denominator by 6

\mathtt{\Longrightarrow \frac{18}{12}}\\\ \\ \mathtt{\Longrightarrow \ \frac{18\div 6}{12\div 6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{2}}

Hence, 3/2 is the standard form of given rational number.

Example 03
Find the standard form of rational number 2.5

Solution

(a) convert decimal into fraction

\mathtt{2.5\ \Longrightarrow \ \frac{25}{10}}

(b) Take HCF of numerator and denominator

HCF (25, 10) = 5

(c) Divide numerator and denominator by 5.

\mathtt{\Longrightarrow \frac{25}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{25\div 5}{10\div 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{2}}

Hence, 5/2 is the standard form of given rational number 2.5

Example 04
Reduce the rational number 0.12 to standard form.

Solution
(a) Convert the number into fraction form.

\mathtt{0.12\ \Longrightarrow \ \frac{12}{100}}

(b) Find the HCF of numerator and denominator.

HCF (12, 100) = 4

(c) Divide numerator and denominator by 4

\mathtt{\Longrightarrow \frac{12}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{12\div 4}{100\div 4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{25}}

Hence, the standard form of given rational number is 3 / 25.

Example 05
Find the standard form of \mathtt{\sqrt{3}}

Solution
Note that \mathtt{\sqrt{3}} is not a rational number.

Hence reduction to its standard form is not necessary.