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Converting Decimals to Fractions and Vice Versa

Converting Decimals to Fractions and Vice Versa 

The process of conversion of decimals to fractions and fractions to decimals will help you a lot while solving sums from varied topics of mathematics. These conversions are employed in almost all the chapters of mathematics and hence it becomes very important that we learn about these conversions very nicely. Before understanding the process of conversion, let us understand briefly fractions and decimals. A fraction can be defined as a number represented in the form of p/q where q is not equal to zero. We use fractions in our real life, knowingly or unknowingly. Examples of it can be one-fifth of the glass of water, three fourth of the cake, etc. Decimals on the other hand are a different method of presentation of fractions on a number line. Their forms are different, however, they are one and the same. 


How Do You Convert Decimals to Fractions?

Converting decimals to fractions is very easy. Let us see how.

  • We will write down the given decimal divided by 1. Example: 0.85/1

  • Now, the operation of multiplication will be carried out on both the numerator and the denominator by 10 for every number after the decimal point. For example: in 0.85 there are two numbers after the decimal. Thus, it will be multiplied by 100.

  • After multiplication, we will get 85/100. Reduce 85/100 to its simplest form.

  • The required answer will be 17/20.

How Do You Convert Fractions into Decimals?

The process of converting fractions to decimals is very easy. Three methods can be employed in the process of converting fractions to decimals. Let us check out all three methods:


By the Help of a Calculator: Let us take an example to see how this can be done. We need to convert 9/4 into decimal. We will press 9 on the calculator and then press the division sign. After pressing the divide sign, we will press 4 and then hit equal to. We will get the answer as 2.25 which is the decimal form.


By the Method of Long Division: We will understand the method of long division by taking an example. We will have to convert 3/4 into decimal. 

  • The process of division of fractions will be carried out in the same manner as that of normal division. Here, the numerator will be treated as a dividend and the denominator will be treated as a divisor. Thus, dividend = 3 and divisor = 4.

  • We observe that the dividend is smaller than the divisor. Here, we will use decimals. We will place 0 at the end of 3 to make it 30 and simultaneously place. (dot) to indicate the use of decimals in the quotient’s place.

  • Now, dividing 30 by 4 will result in the quotient becoming 0.7 with 2 as the remainder. 

  • Once decimal has been used, we can take the help of zero again and again until the remainder becomes zero.

  • Thus, 0 will be placed after 2 to make it 20. Now, 20 will be divided by 4, which will result in the quotient becoming 0.75 and the remainder becoming 0.

  • Thus the required answer in the decimal form will be 0.75.



By the Method of Converting Denominator: This method is useful only when the denominator can be converted to the power of ten. Let us understand this method with the help of an example. We need to convert 6/8 into decimal.

  • We will have to make the denominator to the power of 10. We see that by multiplying 8 with 125 we get 1000, which satisfies our requirement.

  • Thus, 6/8 will become 750/1000 after multiplication by 125.

  • We will now place a decimal point before the number of places equal to zeros in the denominator.

  • Thus, we will place a decimal point before 7. Thus, the required answer will be 0.750 which is in decimal form.


If you want to learn more about converting fractions to decimals or decimals to fractions in detail and in a fun way, follow Cuemath.


A teacher solving decimal fractions on the blackboard


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