Fraction and Decimals

By now, you must have spent hours after completing sums on division. Therefore, you must know that division involves the breaking up of a whole into several parts. For example, consider that you have a whole pizza before you, and you divide it into four pieces. 

So, how are you going to express this situation mathematically? The answer is easy. However, for that, you will have to know what fraction and decimal stand for. 


What is a Fraction? 

A fraction refers to the mathematical representation of equal parts of a whole object. As you have seen in the previous example, you have divided the pizza into four equal parts. In that case, the fractional equation for each slice is:

\[\frac{1}{4}\]

Had you divided into two equal pieces, the fraction would stand as  \[\frac{1}{2}\].

Moreover, 1 refers to the numerator. It indicates the number of equal parts of the whole. On the other hand, 4 and 2 imply the denominator – the total number of equal parts in the whole collection. 

A Quick Sum: 7 out of 10 people ate hamburgers at a party. What is the fraction? 

Notably, you also must know about the types of fractions to understand more about changing fractions into decimals. 


Take a look at the following table to learn about the types of fractions:


What are the Types of Fractions?

Sr. No

Types of Fractions

Definition

Examples

1

Proper Fractions

Proper fractions refer to such fractions where the denominator exceeds the numerator in its numerical value. 

\[\frac{5}{8}\], where 8 (denominator) is bigger than 5 (numerator). 

2

Improper Fractions

In this case, the numerator exceeds the denominator in its value. 

\[\frac{8}{5}\], where 8 (numerator) is bigger than 5 (denominator)

3

Like Fractions

These are such fractions where you can derive at the same value after mathematical simplification. 

\[\frac{1}{2}\] or \[\frac{3}{6}\] or \[\frac{4}{8}\]. Here, the denominator is a factor of the numerator. 

4

Unlike Fractions

Unlike fraction is a set of fractions which vary in their value. 

\[\frac{2}{5}\] and \[\frac{1}{2}\].

5

Mixed Fractions

In this case, a non-zero integer combines with a fraction. 

\[5\frac{6}{7}\], where the fractional expression is \[\frac{(7\times 5) + 6}{7} = \frac{41}{7}\]


In the subsequent sections, you will learn about converting fractions into decimals. However, first you must know what a decimal is. 


What is a Decimal? 

Decimal stands for a mathematical expression which show whole numbers and fractional numbers as separate entities. For instance, consider a decimal number 11.6. In this case, 11 refers to the whole number, and 0.6 implies the decimal. 

So, how do you arrive at a number like that? Look closely:

1.6 stand for 6 parts of a collection of 10 parts. Therefore, \[\frac{6}{10}\] ultimately leads to .6. 

A Quick Sum: Convert 3 parts of 10 whole parts into decimal. 

Now that you know what a decimal is, keep an eye on how to convert a fraction to decimal. 


What is the Process to Convert a Fraction into a Decimal? 

To understand the process to convert fractional numbers to decimal, consider the following steps – 

  • Suppose a proper fraction is \[\frac{5}{8}\], where you will have to divide the numerator 5 with the denominator 8. 

  • Therefore, 8)5 (0.625

                                 - 0

                         ---------------

                                  50

                                - 48

                          ----------------

                                     20

                                   - 16

                           ----------------

                                      40

                                   -  40

                           ----------------   

                                        0

                           ------------------    

Consequently, you have come to know about the first step of conversion involving fraction and decimals. 

However, you might also run into fractions that put forward recurring decimals. In this particular case, the remainder keeps on repeating itself and never comes down to a 0. For instance, consider the following –  

  • \[\frac{4}{9}\] = 4 ÷ 9.

  • 9)4(0.4444

             - 0

            ---------------------

               40

             - 36

            ---------------------

                   40

                 - 36

                   ----------------

                       4

                   -----------------

This is an example of fraction to decimal where the conversion of this specific fraction leads to the formation of a recurring decimal. 

A Quick Sum: Convert \[\frac{7}{11}\] into a decimal and determine whether it is recurring or non-recurring. 

Furthermore, the process to turn a mixed number into decimal is the same. Take into account the following example – 

  • The fraction is \[7\frac{1}{4}\]. Convert it into an improper fraction = \[\frac{(7\times 4) + 1}{4} = \frac{29}{4}\]. 

  • The process of converting mixed numbers into decimals is – 

4)29(7.25

  -28

---------      

10

- 8

---------- 

    20

   -20

----------    

      0

---------

Therefore, the decimal expression of the mixed fraction \[7\frac{1}{4}\] is 7.25. Now, it is the time for converting decimals into fractions. 


How to Convert Decimal to Fraction? 

The process for changing decimals to fractions is quite simple. To understand this, you will have to consider two examples.

Example A is a decimal 0.9, and example B is a decimal 0.75. For a decimal, you will always have to assume the denominator to be 1. 

Therefore, A = \[\frac{0.9}{1}\] and B = \[\frac{0.75}{1}\]. Since A and B have a decimal point before one and two digits respectively, you will have to multiply both the numerator and denominator of A with 10 and B with 100.  

As a result, A = \[\frac{0.9\times 10}{1\times 10}\] and B = \[\frac{0.75\times 10}{1\times 10}\]. 

Thus, A becomes \[\frac{9}{10}\] and B becomes \[\frac{75}{100}\]. However, A cannot be simplified any further because 9 is not divisible by 10. On the other hand, you can simplify B into \[\frac{3}{4}\]. Therefore, this concludes the process for writing decimals as fractions.

On top of that, there is another process that can help you convert recurring decimals into fractions. For instance, consider a recurring decimal 0.77. You can also write it as the following equation – 

  • Suppose x = 0.77. 

  • Multiply both sides with 10. Therefore, the equation becomes 10x = 7.77.

  • Now you will have to subtract x from both sides. The equation thus becomes 9x = 7.

  • Therefore, x = \[\frac{7}{9}\]. 

Thus, the method for turning recurring decimals into fractions becomes quite easy when you consider recurring decimals as x.  

Now you know what fraction and decimals are and how to convert one into the other. However, for further interesting insights into this topic, keep an eye on Vedantu’s website. You can also download our Vedantu app for easier access.

FAQ (Frequently Asked Questions)

1. What is a Fraction?

Ans. A fraction is a mathematical expression that consists of a numerator and a denominator. In this case, the denominator refers to the total number of parts in a whole. On the other hand, the numerator stands for the number of parts in question from the whole. For example, in the fraction 2/5, 5 refers to the total number of parts, and 2 is a section of the entire entity. 

Fraction can be used to represent ratios and divisions as well. You might also find negative fraction which is often used to represent loss.

2. What is a Decimal?

Ans. Decimal stands for an expression where the whole number and the fractional number are shown separately. The expression consists of a decimal point (.) that divides the two parts. The example of a decimal is 5.667, where 5 is the whole number and 0.667 is the fractional part.

Numbers that are represented via decimal system are called decimal fractions. Modern mathematics allows for infinite decimals which is used to represent any real number. You can introduce an infinite sequence of digits following the decimal denominator. Infinite decimals represent rational numbers only if it has non-zero digits.

3. What is a Mixed Fraction?

Ans. Mixed fractions imply the combination of a whole number and a proper function. However, the whole number has to be a non-zero integer. Besides, the numerator also has to be lower than the denominator for it to be a proper fraction. An instance of a mixed fraction is 5 9/11. 

You can operate normal mathematical processes, including multiplication, division, addition, and subtraction while working with mixed fraction. Other than mixed fraction, you will also come across proper fraction and improper fraction in this chapter.

4. What is a Recurring Decimal?

Ans. Recurring or repeating decimal refers to the mathematical representation where the digits are primarily periodic. It suggests that the digits after the decimal point simply recur themselves in an infinite manner. In this case, the remainder from the division of the numerator by the denominator is never zero. 

Rational numbers are either a repeating decimal, or a terminating decimal. If 0 does not come as a remainder, you can continue with the division process. The repeating sequence is known as repetend; it has a certain value higher than 0.