Convert Decimal to Fraction

A number is a numerical value that is used to represent the quantity/measurement of an object like to represent the weight of a person, length of a geometric shape, value for the money, etc. Numbers can be classified into many types. Some of them are decimal numbers, integers, rational numbers, complex numbers, etc.

Decimal Number

A number can be considered as a decimal number such that any integer part and fractional part are separated by a decimal point. When the weight of a person/thing is measured always it’s not possible to represent in real numbers like 50, 55, etc. Sometimes it may be greater than 50 and less than 51 at that point decimal numbers can come into action.

Example: 0.619, 50.5, etc.

Fraction

A number that is expressed in the form of a/b form can be called a fraction. Where a, b are any numbers. Fraction is a (quotient) number expressed in the form of a numerator divided by a denominator. Rational numbers, Irrational numbers are considered fractions.

Example: 619/1000, etc.

Let’s consider a Decimal value c and this decimal c can be converted into fraction a/b such that on solving of a/b gives result c. 

c = a/b

Where c is a decimal number, a/b is a fraction.

To convert a decimal number to a fraction we need to follow a sequence of steps.

Decimal to fraction Conversion

There are certain steps that are needed to be followed in order to convert a decimal number into a fraction. Let’s take a look at these steps,

Step 1: First, divide the decimal number by 1.

Example: Decimal number 0.72 

On applying step 1 0.72/1 is obtained.

Step 2: For every decimal point in the numerator multiply 10 for both numerator and denominator.

In this example, 2 numbers are given after the decimal point, so multiply with 10 two times for both numerator and denominator.

0.72 × 10 × 10/1 × 10 × 10 = 72/100

Step 3: Perform simplification on the fraction formed from Step – 2 until further simplification is not possible.

72/100 

= 36/50 

= 18/25

These are the 3 steps that one must follow while converting from decimal to fraction.

Let’s look into some examples to get more clarity on it.

Sample Problems

Question 1: Convert a decimal 0.1 to a fraction

Solution:

Step – 1 Divide decimal with 1

= 0.1/1

Step – 2 As there is only 1 number after point so multiply 10 one time to both numerator and denominator.

= 0.1 × 10/1 × 10 = 1/10

Step – 3 The above generated can’t be simplified further so we consider the above fraction 1/10 as final result.

So fraction of 0.1 = 1/10

Question 2: Convert a decimal 6.25 to a fraction

Solution:

Step – 1 Divide decimal with 1

= 6.25/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 6.25 × 10 × 10/1 × 10 × 10 = 625/100

Step – 3 This 625/100 fraction can be simplified to,

625/100 = 125/20 = 25/4

So fraction of 6.25 = 25/4

Question 3: Convert a decimal 6.25 into a mixed fraction.

Solution:

When a whole number is present before point in decimal number then separate that whole number from decimal number and follow the 3 steps for conversion.

6.25 = 6 + 0.25

Step – 1 Consider the digits that are after the decimal point i.e., 0.25 and Divide decimal with 1

= 0.25/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 0.25 × 10 × 10/1 × 10 × 10 = 25/100

Step – 3 This 25/100 fraction can be simplified to

25/100 = 5/20 = 1/4

Add the separated digit 6 (done before step-1) to formed fraction.

So fraction of 6.25 = 

Question 4: Convert a decimal 4.372 into a mixed fraction.

Solution:

For conversion into mixed fraction, separate the whole number part before the decimal point from decimal value and follow the above specified 3 steps on numbers after decimal points.

4.372 = 4 + 0.372

Step – 1 Consider the digits that are after the decimal point i.e., 0.372 and Divide decimal with 1

= 0.372/1

Step – 2 As there are 3 numbers after point so multiply 10 three times with both numerator and denominator.

= 0.372 × 10 × 10 × 10/1 × 10 × 10 × 10 = 372/1000

Step – 3 This 372/1000 fraction can be simplified to,

372/1000 = 93/250

Add the separated digit 4 (done before step-1) to formed fraction

So fraction of 4.372 =  

Question 5: Convert a decimal 0.33 to a fraction

Solution:

Step – 1 Divide decimal with 1

= 0.33/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 0.33 × 10 × 10/1 × 10 × 10 = 33/100

Step – 3 This 33/100 fraction can’t be simplified so it can be leaved as it is

So fraction of 0.33 = 33/100 

Question 6: Convert a decimal 0.3333… to a fraction

Solution:

Step – 1 Divide decimal with 1

= 0.3333…./1

Note: For this kind of recurrence number i.e., 3 is recurring for infinite times we can’t multiply 10 for each decimal point. In this case we multiply numerator and denominator with 3.

Step – 2 As this is a recurrence number we multiply 3 with numerator and denominator.

0.3333…. × 3/1 × 3 = 0.9999…./3

Step – 3 Simply the above fraction.

As 0.9999… is close to 1, round up the numerator to 1.

0.9999…./3 can be simplified to 1/3.

So fraction of 0.3333… = 1/3