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**

Follow the below steps;

(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**

Follow the below steps;

(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.