Math Concepts

Decimals to Fractions to Percentages - The Relationship Between Them

May 24, 2020

Reading Time: 5 minutes

One of the most important basic fundamental concepts of the number system is decimals and fractions. They both actually mean the same. But, the difference lies in the way of presenting a number. 

In the number system tree, we have two types of numbers:

Integers:- It refers to whole numbers, either positive or negative. These numbers don’t have a fractional component. Examples are {-1, -4, -99} or {1, 5, 78} etc.

Decimals:- It refers to numbers that have both an integer and a non-integer part. These parts are differentiated by a decimal point. Examples are {2.5, 10.99, 34.7697} etc. The part after the decimal point is known as the fractional part and the part before the decimal point is known as the whole number part.


important notes to remember
Important Notes
  1. There can be only one decimal point. 

  2. There can be either a fixed or an endless number of digits after a decimal point.

  3. Whole numbers can also be written in the form of decimals by writing 0 on the right side of the decimal point. For example - 10.0 or 23.00 etc.

The numbers which are decimals by nature can be represented in the form of fractions. For example, 0.5 can also be written as 5/10. This can be reduced to the lowest form to get 1/2. 

Another very important basic concept is the percentage. Percentages refer to decimal numbers to the base 100. These are represented by a % (percent sign). For example, 35% when converted into fraction will be 35/100. This can be written as 0.35 in decimal terms.


These 3 concepts share a strong inter-relationship with each other. The article focuses on the step by step approach of understanding these relations and conversions between decimals, fractions, and percentages. The topic further has been divided into six categories, with their respective explanations.

  1. Decimals to Fractions:

Step 1: Write the decimal number as the numerator. 

Step 2: Remove the decimal point

Step 3: In the denominator write 1 followed by number of zeros equal to the number of digits that were there after the decimal point 

Step 4: Reduce the number to the lowest form

This way you can convert a decimal to fraction in a step-by-step manner.

Example 1

 

 

Convert 62.520 to a fraction

Step 1 and 2- Write 62.520 as 62520 in the numerator

Step 3- Write 1000 in the denominator

Step 4- 62520/1000 should be reduced to the lowest form which will be 1563/25

Example 2

 

 

Convert 0.333 to a fraction

Step 1 and 2- Write 0.333 as 333 in the numerator

Step 3- Write 1000 in the denominator

Step 4- 333/1000 should be reduced to the lowest form. This cannot be further simplified, so this is the final answer.


  1. Fractions to Decimals:

Method 1 (Always applicable): Make the numerator as the dividend and the denominator as the divisor. Now it becomes a simple division problem. The quotient derived will be the answer. This way you can convert a fraction to decimal in a step-by-step manner.

Example 1

 

 

Convert 7/25 into a decimal

25)70(0.28

     50

  ---------

   200

   200

  ---------  

     0

In the above example, 7 became the dividend and 25 became the divisor. It was solved like a normal division problem, as shown. 0.28, which is the quotient, is the decimal format of the fraction 7/25, and thereby the final answer.

Method 1 (Applicable when the denominator can be converted into a multiple of 10):

Step 1: Multiply the numerator and the denominator by the same number so that the denominator becomes a multiple of 10 

Step 2: Write the top number by properly adjusting the point. The number of digits after the point must be equivalent to the number of zeros in the denominator.

This way you can convert a fraction to decimal in a step-by-step manner.

Example 2

 

 

Convert 3/4 into a decimal

Step 1- Multiply 3/4 by 25, both numerator and denominator. It becomes 75/100.

Step 2- Place the decimal point by keeping 2 digits to the right of the point. The answer will be at 0.75.


  1. Fractions to Percentages:

Step 1: Make the numerator as the dividend and the denominator as the divisor. Now it becomes a simple division problem.

Step 2: Multiply the quotient by 100

This way you can convert a fraction to percentage in a step-by-step manner.

Example 1

 

 

Convert 12/25 into a percentage

25)120(0.48

     100

  ---------

     200

     200

  ---------  

       0

In the above example, multiply 0.48 by 100 which becomes 48. This will be represented as 48%.

Example 2

 

 

Convert 13/5 into a percentage

5)13(2.6

   10

---------

   30

   30

---------  

    0

In the above example, multiply 2.6 by 100 which becomes 26. This will be represented as 26%. 

 


  1. Percentages to Fractions:

Step 1: Remove the percent sign and write 100 in the denominator

Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point.

Step 3: Simplify to the reduced form

This way you can convert a percentage to a fraction in a step-by-step manner.

Example 1

 

 

Convert 50% into a fraction

Step 1- Write 50% as 50/100.

Step 2- 50 is a whole number so step 2 can be skipped. 

Step 3- 50/100 can be reduced to 1/2 which is the answer. 

Example 2

 

 

Convert 62.25% into a fraction

Step 1- Write 62.25% as 62.25/100.

Step 2- This can be written as 6225/10000 by multiplying 100 in both the numerator and the denominator

Step 3- Reduce it to the simplest form. The answer will be 249/400.


  1. Decimals to Percentages:

Step 1: Multiply the decimal by 100 or simply shift the decimal point 2 steps towards the right and attach a percent sign.

This way you can convert a decimal to percentage in a step-by-step manner.

Example 1

 

 

Convert 5.1 into a percentage

Step 1- Perform 5.1*100 which will result in 510%.

Example 2

 

 

Convert 0.0123 into a percentage

Step 1- Perform 0.0123*100 which will result in 1.23%.


  1. Percentages to Decimals:

Step 1: Remove the percent sign and write 100 in the denominator

Step 2: Remove the denominator and place the decimal point in the numerator by 2 places to the left

This way you can convert a percentage to a decimal in a step-by-step manner.

Example 1

 

 

Convert 35% into a decimal

Step 1- Write 35% as 35/100.

Step 2- 35/100 will be written as 0.35

Example 2

 

 

Convert 120.25% into a decimal

Step 1- Write 12.25% as 12.25/100

Step 2- 120.25/100 will be written as 1.2025


We hope this article and the step by step approach explained herein was useful for our readers.

Cuemath tries to explain all the concepts to its students in a similar fashion. Firstly, it uses practical examples to which students can relate to. Secondly, it breaks a numerical into different steps that are easy to understand. Finally, it provides students with enough assignments and numerical, so that they can undergo regular practice. Various puzzles, assignments, and mind games are also available on the Math Gym App offered by Cuemath. This is available for both our Android and iOS users. We provide our entire support to students by providing them with timely updates to their doubts and solutions.

Happy Studying!!

Best of luck!!

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