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How To Convert Decimals To Fractions?

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  1. Introduction 

In mathematics, for a given value of a fraction, defining the whole number is a part of solving an equation. A value in a fraction can be stated as a ratio of two numbers, “x” and “y”. In which the number is a decimal, Here a whole number is a part and the fractional part of that number representation is separated by a unit decimal point. 

While solving any given equation, the preferred way of solving is by converting decimal valued function to fraction, as it's generally known fractional valued functions are easy to solve. In this article, we will learn how to convert decimals into fractions in an easy way, and some of the common conversion values are provided.

Before getting started with easy conversion of a value from decimal to fraction, the first step is to understand the definition and representation of decimals and fractions, 

  1. Fraction Definition

A fraction is an expression of one number over the other numerator and denominator. It can be represented as “XY”. The upper value “x” in the fraction is called a numerator and the number below in the fraction “Y” is called a denominator. In practical, there are three types of fractions, 

  • Proper Fraction- when a numerator value is smaller than the denominator value, 

Example: 45

  • Improper Fraction- Here, the opposite of the proper fraction, the denominator value is greater than the numerator value, Example: 54

  • Mixed Fraction- It's the combination of proper fraction and whole number, 

While a mixed fraction can be converted to improper fraction, 

Example: 413

  1. Decimal Definition 

A decimal can be defined as a numerical, written using a decimal notation, and these numbers are generally adopted to the values that combine a fractional part and whole numbers, which are segregated using the decimal separator from the integer side.

Example: 1024.6

The above number has 1 thousands , 0 hundreds , 2 tens and 4 ones and 6 tenths.

Types of decimals, 

  1.  Repeating or Non-Terminating Decimals (Recurring decimals)

Here the occurrence of the number in digit is repeating 

3.1251525 (Finite number)

3.454545454545 (Infinite number)

  1. Non Repeating or Terminating Decimals (Non-Recurring Decimal Numbers)

The repeating pattern with the numerical is not observed in this type of decimal.

3.1871 (Finite)

3.65729090….(Infinite)

  1. Repeating decimals and terminating decimals conversion

Any decimal number, even a complicated-looking number, can easily be converted to a fraction; step by step procedure needs to be followed. In the Below section you can see the explanation and steps to convert both repeating decimals and terminating decimals to fractions. 

First let's see , conversion of Terminating Decimal number to a Fraction number. 

A terminating decimal number is any decimal number that has a finite order of digits. Also, it can be stated that number which has an end. Examples include .4, .123, .76767, etc. Terminating decimal numbers are general and common decimals you’ll observe during your calculation, fortunately, one of the easiest one to convert.

Step 1:

For the given decimal number divide it by 1. 

Consider a decimal 0.22 and now divide it by 1, it looks like 0.221

Step 2: 

Next, you should multiply the numerator and denominator of the fraction by number 10 with the every digit from the left of the decimal point.

In the example provided above .22 consists of 2 digits 22 after the decimal point, now both the top and bottom needs to be multiplied with 1010= 100 

Now the equation looks like, 1001000.221= 22100

Step 3: 

Converting the equation to the simplest form

Now take an example, 25100which is 14Well that is a simple equation, same way our equation needs to be reduced. 

Considering our equation, 22100now multiply both the top and bottom with 2 

221002 2= 1150 as 11 is the prime number it cannot be reduced.

Example, Above conversion of a simple equation was considered, now to provide a proper example. Lets convert 0.208 to fraction, let's follow all the steps stated above, 

  1. Divide the equation by 1 , 0.2081

  2. Now multiply 101010 as there are 3 numbers after the decimal. That will be 1000 multiplication for top and bottom, 2081000

  3. Simplifying the equation, 26125

It's recommended to practice with large numbers. 

E. Converting Repeating decimals to fraction

Recurring number, or number which has no end. As the number cannot be written forever it needs to round off. Example value of pie 3.1323167678.. Or round off to 3.14. Now consider 0.534344 repeating number , Which is represented as 0.5333333= 0.5 a line on top. 

Now lets convert 0.55568 to a fraction, 

It is represented as 0.5 , 0.555, 0.555687 etc, these all are the representation of the number and string goes forever, 

Step 1: 

Now consider x has equal to the repeating number that we have considered 

x=.5557

Now here 5 is the repeating digit, to round up the last decimal is considered. 

Step 2

Now calculate, by how many times multiplication has to be done with 10 to get the repeating number on to the left of the equation, simple as moving the decimal by one one spot. Now if we multiply it with 10 on both the sides. 

10x=5.557

Remember, you only require one digit to the left side of the decimal. As in this equation 5 is the repeating one, only 5 is brought to the left. If the number is .65656565 then you would require to move two digit thats one set “65” 

Step 3 

In this step you should see that any repeating digit (5) should be on the right of the decimal, that equals to x

x= 0.5557, there is no multiplication or calculation involved in this step, 

Step 4

Now, Finding the value of x by considering both the equation, 

10x-x=5.557-.5557

9x=5

x=59

It looks a little tricky but with little practice, you can ease the conversion. 

Example: 

Converting 1.0464646

Well with the first observation we can say the above number belongs to repeating number, with step by step we will be able to solve the equation, 

To move the repeating number you need to multiply 3 times, (10 3) 

That equals to the 1000, multiply 1000 on both the sides of the equation, 

1000x=1046.4646

Now following step 3, moving the repeating digits to the right of the decimal. Equation considered here is x= 1.0464646. Now we can see that zero is between the decimal and the repeating number. So multiply 10 on both the sides, sa

That gives 10x=10.464646

Now combining both the equation to find the value of x

That equals, 1000x-10x=1046.464646- 10.464646

990x=1035

x=1035990=2322

To convert negative decimal to fraction, 

  • First, the negative sign needs to be removed from the negative decimal number.

  • Next, perform the conversion as the same as a positive decimal.

  • At last, apply the negative sign to the converted fraction value. 

To represent ,if  x=y is true then -x=-y

F. Most used Decimal to Fraction Conversions

In the Below table you can observe commonly used decimal to fraction conversions. These need not be memorized, but this will aid during your regular calculation, making the conversion calculation faster. Also, this table can be used as a reference table if the calculator is not accessible, as shown below in the table each value in this chart, for which there is a number closest to that so you can make quick estimation during the conversion.

Decimal 

Fraction

0.0625

116

0.03125

132

0.16667

16

0.125

18

0.1111

19

0.1

110

0.25

14

0.222

29

0.2

15

0.375

38

0.3333

13

0.3

310

0.4444

49

0.4

25

0.5555

59

0.5

12

0.666

23

0.625

58

0.6

35

0.777

79

0.75

34

0.7

710

0.888

89

0.875

78

0.8333

56

0.8

45

0.9

910

G. Summary: converting Decimal Into a Fraction

If you’re learning to convert from a given decimal value to fraction value, primarily you need to identify if the given value has a terminal decimal (number at the end) or a recurring decimal (number in a digit of infinite value). Upon completion of this step, the above said steps need to be followed to make the required value conversion into fraction. To learn Numbers Tips and Tricks like the one explained above, refer to cuemaths.

In reverse, to convert a fraction to a decimal, the best way is to make use of your calculator. In rare cases, if a calculator is not available, it's recommended to use long division or make the denominator value equal to a multiple of ten, later make changes to the decimal place of the numerator. 

For better and quick reference during the conversion of decimal to fraction (or vice versa), you can refer to the table provided above of common value conversions and check for the value which is closest. For quick and easy conversion of a decimal value to a fraction, it's advantageous to use the conversion calculators. 

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