How to Convert Decimal to Fractions? With Examples & Chart

Posted on May 22nd, 2021
Convert Decimal to Fractions
Convert Decimal to Fractions (With Examples & Chart)

How to Convert Decimal to Fractions? With Examples & Chart

Convert Decimal to Fractions

To convert decimal into a fraction, we should first write the given decimal in such a way that decimal numbers should be written as numerators with 1 as a denominator. Then multiply both numerator and denominator with the multiples of 10, in order to remove the decimal from the given number. For e.g., we have 2.7 as a decimal number, such that the equivalent fraction becomes 27/10. However, there is no further simplification of 27/10.

 

What do you mean by Decimal and Fractions?

In computer terms, decimal numbers are numbers with a base often. However, in Mathematics, a decimal number is a number with a “.” (dot) or decimal point between the digits. Normally, decimals are nothing but fractions with denominators as 10 or multiples of 10. For example, 3.2, 10.9, 55.1, 1.28, 9.234, are decimals.

Fraction is a part of a whole number. It is denoted as a ratio of two numbers a/b, where both “a” and “b” are integers, and also b≠0. Integer “a” is called a numerator and integer “b” is called a denominator. For e.g., 2/3 is a part of 2, 4/5 is a part of 4, etc. on fractions; we can execute all arithmetic operations. Proper, Improper, and Mixed fractions are the three categories of fractions.

Decimal to Fraction Chart

With anchor charts, fractions and decimal conversion becomes crystal clear and more understandable.

Chart representing some commonly-used fractions and their decimal equivalents:

Decimal Equivalent Fraction Simplest Form of Fraction
0.1 1/10 1/10
0.125 125/1000 1/8
0.25 25/100 1/4
0.75 75/100 3/4
0.875 875/1000 7/8
1.125 1125/1000 9/8
1.25 125/100 5/4
1.5 15/10 3/2
1.75 175/100 7/4
1.875 1875/1000 15/8

 

Conversion of Decimal to Fraction

simple steps to convert a decimal to a fraction
Conversion of Decimal to Fraction

 

Follow these three simple steps to convert a decimal to a fraction.

Now, we are using decimal 0.25 as an example.

Step 1: The decimal number needs to be rewritten over one (as a fraction where the decimal number 0.25 is the numerator and place 1 as the denominator).

Step 2: Multiply both the numerator as well as the denominator by 10 to the power of the number of digits after the decimal place. If there is one value after the decimal, multiply by 10, if there are two then multiply by 100, if there are three then multiply by 1,000, and so on.

However, for converting 0.25 to a fraction, there are two digits after the decimal point. Since 10 to the power 2 (102) is 100, we have to multiply both the numerator and denominator by 100 in this step.

Step 3: Now, express the fraction in the reduced form (or simplest form).

0.25 =  0.25/100 = 0.25 x 100/ 1 x 100  = 25/100 = 25/5/100/5 = 5/20 = 5/5/20/5 = 1/4

The above three steps should be followed in the decimal to fraction conversion; you can conclude that the decimal 0.25, when converted to a fraction, becomes equal to 1/4.

 

Some important Examples

  • Find the fraction form of the decimal 0.9

We have, decimal number 0.9, we need to find the fraction for 0.9.

A number of equivalent fractions can also be found by finding its multiples.

0.9 x 2 (10 x 2) = 18/ 20

Now multiply, 9/10 by 2, both in numerator and denominator, then we get;

To find more equivalent fractions, let us multiply 9/10 by 5 and 10 both in numerator and denominator.

9 x 5 / 10 x 5 = 45/50

And

9 x10 / 10 x 10 = 90/100

Thus, the fractions of 0.9 decimal are 9/10, 45/50, and 90/100.

 

  • Convert 6.45 into a fraction.

We have, 6.45 is a decimal number.

Multiply and divide 6.45 by 100.

6.45x 100 /100 = 645/100

If we simplify it more, we get;

129/20

Now, find the equivalent fractions by multiplying both the numerator and denominator by 2, Such that;

129 x 2 /20 x 2 = 258/40

Therefore, 6.45 equivalent fractions are 645/100, 129/20, and 258/40.

 

  • Convert 4.45 into a fraction.

Follow the steps, place 1 as a numerator.

4.45/1

Since there are two numbers after the decimal point, then, multiply 4.45/1 by 100 in both numerator and denominator.

(4.45/1) x (100×100) = 445/100 = 89/20

  • Convert 1.875 into a mixed fraction.

Write 1.875 as 1.875/1

To remove the decimal up to three places, multiply by 1000.

(1.875/1) x (100 x 100) = 1.875 x 1000

Simplifying 1875/1000 we have;

⇒ 15/8 = 1 7/8

Now, the mixed fraction becomes

Thus, 1 7/ is the mixed fraction equivalent to 1.875.

  • Convert 0.3333… into a fraction.

Let x = 0.3333

On both sides, multiply x by 10.

10 x = 3.333…

Subtracting x from 10x, we have;

10xx = 3.333…-0.3333

9x = 3.000

x = 3/9 = 1/3

Hence, 0.3333… = 1/3

 

 Must Check Factors of 48 and Pair Factors of 48

 

Some important FAQs

Write 0.875 as a fraction.

Place 1 as a denominator, and multiply both numerator and denominator by 1000.

(0.875/1) x (1000 x 1000) = 875 x 1000 = 7/8

0.875 is equivalent to 7/8 as a fraction.

 

Write 2.25 as a fraction.

Place 1 as the denominator, and multiply both numerator and denominator by 100.

(2.25/1) x (100 x 100) = 225 x 100 = 9/4

2.25 is equivalent to 9/4 as a fraction.

 

Write 0.225 as a fraction.

Place 1 as a denominator, and multiply both numerator and denominator by 1000.

(2.225/1) x (1000 x 1000) = 225 x 1000 = 45/200 = 9/40

Thus, the fraction form is 9/40.

 

How a decimal number can be converted into a fraction?

The decimal number to be written in the form p/q, such that q=1. Now, multiply and divide both numerator and denominator by 10n until n decimal places. Now, simplify the fraction obtained.

 

How to write decimal into mixed fraction form?

Suppose that 2.7 is a decimal number. Write the decimal into fraction form as 2.7/1. Now, multiply both numerator and denominator by 10, such that (2.7/1) x (10/10) = 27/10. 27 divided by 10 is 2 with 7 as a remainder. Thus, 27/10 can be written as 2 7/10 in mixed fraction form.

 

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Takshila learning helps you in converting decimals to fractions  

 

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