In this post we will understand how to convert fraction into decimal.

We have discussed 4 methods to convert fraction into decimal. Try to learn each of the methods and practice the ones which you find easy and practical to use.

After the concept, we have solved some worksheet problems. I urge you to solve each of the questions first and then look for the solution given in the end.

**Methods to convert Fraction into Decimal**

Given below are the four methods which you can use as per the given situation.

The methods discussed are:

(A) When Fraction contains 10, 100, 1000 etc. as denominator

(B) Long Division Method

(C) Converting Denominator into 10, 100, 1000 etc..

(D) Denominator is any random number with 0 at the end

**(A)** **When denominator of fraction contains 10, 100, 1000, 1000 etc..**

In this case, we will follow below steps:

(i) First count the number of zeros in denominator

(ii) Write the numerator

(iii) Count digits from right and put decimal point leaving same number of digit as number of zeros in denominator

Let us understand the concept with examples:

**Example 01****Find decimal of fraction**

\Longrightarrow \ \frac{555}{100}

**Solution**

(i) There are two zeros in the denominator

(ii) In the numerator we will leave two digits from right and put decimal point

So the fraction is ⟹ **5.55**

**Example 02****Find the decimal of fraction**

\Longrightarrow \ \frac{629}{10}

**Solution**

(i) There are one zero in the denominator

(ii) Leave one digit from right and put decimal point in numerator

The fraction is ⟹ **62.9**

**Example 03**

Find the decimal of fraction

\Longrightarrow \ \frac{754}{1000}

**Solution**

(i) There are three zeros in denominator

(ii) Count three digits from right and then put decimal point in numerator

The decimal will be ⟹ **0.754**

**Example 04****Find the decimal of fraction**

\Longrightarrow \ \frac{5}{100}

**Solution**

(i) There are two zeros in denominator

(ii) But there is only one digit in the numerator (i.e. 5)

Make it two digit by adding 0 at the front

Now the numerator is **05**

(iii) Count two digits from the right and put decimal point in numerator

The decimal is ⟹ **0.05**

**(B) When denominator of fraction contain any other random number**

In this case we have to use long division method, the convert the fraction into decimal.

Let us understand this with the help of examples:

**Example 01**

Find the decimal of fraction:

\Longrightarrow \ \frac{61}{5}

**Solution**

As denominator is not 10, 100, 1000 etc….

We will use **long division method**

Hence the required decimal is ⟹ **12.2**

**Example 02**

Find the decimal of fraction

\Longrightarrow \ \frac{1}{2}

**Solution**

As the denominator does not contain 10, 100, 1000 etc..

We will use Long Division method

Hence **0.5** is the required decimal

**Example 03**

Find the decimal of the fraction

\Longrightarrow \ \frac{5}{8}

**Solution**

Finding the decimal using long division method

Hence, **0.625** is the required decimal

**Example 04**

Find the decimal of the fraction

\Longrightarrow \ \frac{13}{2}

**Solution**

Finding decimal using long division method

Hence 6.5 is the required decimal

**(C)** **Converting Denominator into 10, 100, 1000, etc.**

If you don’t want to use long division method. Try to multiply a number with denominator to make it 10,100, 1000 etc . After that wan continue the fraction conversion using Method 1.

⟹ This method works best when the denominator contains number which is power of 2

**Example 01**

Convert following fraction into decimal

\Longrightarrow \ \frac{115}{2}

(i) If we multiply 2 with 5, the number becomes 10

So multiply numerator an denominator by 5

Fraction becomes

(ii) Now the denominator contains 10, we can convert the fraction into decimals using Method 1

⟹ Count one digit from right and place decimal in numerator

**Example 02**

Convert the following number into decimal

\Longrightarrow \ \frac{5}{16}

Solution

(i) If we multiply number 16 with 625, we get number 10,000

So multiply numerator and denominator by 625, the fraction becomes:

(ii) Now the denominator contains 10,000; you can solve the fraction using method 01

Number of zeros in denominator = 4

So count 4 digits from right and put decimal point in the numerator

**Example 03**

Convert the following fraction into decimal

\Longrightarrow \ \frac{15}{4}

Solution

(i) If we multiply 4 with 25 we get 100

So multiply numerator and denominator by 25

(ii) Now denominator contains 100, convert the fraction into decimal using method 01

Number of zeros in denominator = 2

Count two digits from right and place decimal in numerator

**(D) When denominator contains random number with 0 at the end**

When the denominator is multiple of 10 like 20, 30, 90, 120, 190 etc.., use the following steps

(a) First separate the zeros and non zeros in denominator

(b) Divide the numerator and non zero denominator using long division method

(c) After division, use method 01 using the zero left in denominator

Let us understand this using example

**Example 01****Convert following fraction into decimal**

\Longrightarrow \ \frac{24}{20}

**Solution**

In the denominator, the number is multiple of 10; So we will use method 05

(i) Separate non zeros and zeros in denominator

(ii) First divide (24/2) using long division method

Here we get 12 as solution

This division can also be expressed as following:

(iii) Now divide 12/10 using method 1

⟹ Number of zero’s in denominator =1

⟹ So we will leave one digit from right and place decimal in numerator

Hence, **1.2 is the solution**

**Example 02****Convert the below fraction into decimal form**

\Longrightarrow \ \frac{13}{50}

Solution

(i) Separate zeros and non zeros in the denominator

(ii) Divide 13/5 using Long division Method

Hence 2.6 is the solution of above division.

This can also be shown as follows:

(iii) Now divide 2.6/10 using method 1

⟹ Number of zero’s in denominator = 1

⟹ From existing decimal point shift the decimal point by one digit

Hence, **0.26 is the solution**

**Example 03****Convert the fraction into decimal**

\Longrightarrow \ \frac{156}{120}

Solution

Denominator is multiple of 10, so use method 5 for decimal conversion

(i) Separate zeros and non zeros in denominator

(ii) Divide (156/12) using Long Division Method

Here 13 is the solution

The division can be expressed as:

(iii) Divide 13/10 using Method 1

⟹ Number of zeros in denominator =1

⟹ Leave one digit from right and place decimal point

Hence, 1.3 is the solution

**Fraction into decimal Worksheet**

Given below are collection of questions related to conversion of fraction to decimal.

All the questions are to the standard of Grade 5 Math.

Each question is provided with detailed solution.

(1) **Convert 3/5 into decimal**

Using Long Division Method

**Hence 0.6 is the solution**

(02)** Convert 3/4 into decimal**

Using Long Division Method

**Hence, 0.75 is the solution**

**(03) Find fraction for decimal (9/1000)**

Read Solution

We will use method 1 of fraction to decimal conversion

(i) Number of zeros in denominator = 3

(ii) From right start counting digits and place decimal after third digit

**Hence 0.009 is the solution**

**(04) Find fraction for decimal (18/25)**

Convert fraction into decimal using Long division method

Hence, **0.72 is the solution**

**(05) Find decimal for (132/10)**

Using Method 1

(a)Number of zero in denominator =1

(b) Count one digit from right and put decimal point

Hence, **decimal 13.2 is the solution**

**(06) Find the decimal for (4/20)**

we will use method 4 to convert the fraction into decimal

(i) Separate the zero and non zero digit of denominator

(ii) Divide (4/2) using long division method

We get 2 as a solution.

The division can also be expressed as follows:

(iii) Divide 2/10 using Method 01

Hence, **0.2 is the solution**

**(07) Find the decimal for ⟹ 55/10000**

Divide 55/10000 using Method 1

Number of Zeros in Denominator = 4

Leave 4 digit from right and put decimal point in numerator

**Hence 0.0055 is the solution**