Fraction into decimal

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

2^{1} =2\\ \\ 2^{2} =4\\ \\ 2^{3} =8\\ \\ 2^{4} =\ 16 \ \ \ etc..

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

Read Solution

(02) Convert 3/4 into decimal

Read Solution

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

Read Solution

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

Read Solution

(05) Find decimal for (132/10)

Read Solution

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

Read Solution

(07) Find the decimal for ⟹ 55/10000

Read Solution