Number Series

Decimal Fractions


Students in exams face difficulty while solving the questions for decimal fractions. This is because they are not sure of the formula to use while solving the decimal fractions questions. It is necessary to understand the concept so as to be able to solve it during the exams. There are different formulas for decimal fractions which you need to remember while solving the questions. 

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Decimal Fractions

Fractions: The number which is of the form a/b, where b is not equal to 0, is termed as a fraction. In this case, a and b are termed as the numerator and denominator of the fraction. A fraction is also a rational number. So, the fraction will be,


The fraction represents some part of a number or a whole number generally. This number is divided into equal parts.

Thus, when a number is divided into ‘n’ number of equal parts, then one or more is termed as a fraction of that number.

The numerator defines a number that is equal parts and the denominator represents how many parts will that number make up to. Some of the points that you need to remember in the fractions are:

  • When the value of a fraction a/b = 1, then denominator = numerator.
  • If the denominator is 0 then the value of the fraction will be infinity.
  • The value of denominator is not 0 and the value of numerator is 0, then the fraction = 0.
  • If the value for the numerator and denominator is divided and multiplied by the same number, then the value of the fraction does not change.
  • A decimal fraction is called a pure recurring decimal when the number after the decimal keeps on repeating.
  • Also, a decimal fraction is called mixed recurring decimal when some of the numbers are repetitive and some numbers are not.

Browse more Topics under Number Series

Learn more about Missing Number Series here in detail.

Types of Decimal Fractions

The fraction is called a decimal fraction where the power of denominator is 10. For example, the 10th part of a unit i.e. 1/10 = 0.1.

When you convert decimal into a simple fraction, put 1 in the denominator under the decimal point. After this, remove the decimal point and place as many numbers of zeros after the decimal point.

Also, reduce the fraction in its smallest form.

For example, 476/100 = 119/25

Different Functions of the Decimal Fraction

  1. For subtraction and addition, write decimal functions in such a way that they are in the aligned form. It will be easier to solve the equations.
  2. For multiplying two or more decimal functions, multiply them without considering the decimal points. After this, mark the decimal points for as many places as the sum of the decimal numbers is given.

For example: Multiplying 4.3 x 0.13 is,

First, remove the decimals. So, this will be 43 x 13 which is equal to 599. Now add the decimal points.

Here it is 1 + 2 = 3. Put the decimal on the left side of 599 which will be 0.599. So, 4.3 x 0.13 = 0.599.

Similarly, repeat the steps for the division.

  1. LCM and HCF of decimal fractions

For LCM, first, make sure that the decimal point of each and every number is the same. Now, find the LCM of the numbers as if they are the integers. Follow the same procedure as you do in an integer. Also, for the result, do not forget to mark the decimal places equal to the ones given in the numbers.

Example: Find LCM for 9.6, 0.8, and 0.12.

The numbers given above are the same as 9.60, 0.80, and 0.12.

Now, find the LCM for 960, 80, and 120. It will be 960. So, the required LCM for the above three numbers is 9.60.

For HCF also, follow the same procedure. Instead of LCM, you need to find HCF over here.

Example: Find the HCF of 0.90 and 15.5.

The numbers given here are the same as in 1550 and 90. So, HCF of 90 and 1550 is 10. Therefore the HCF of 0.90 and 15.5 is 0.1.

Practice Questions

Q. Find the number of digits that will be on the right side of the decimal point for the product of 0.5567 and 82.56.

A. 6                     B. 5                    C. 7                    D. 3

Answer: C. 7

Q. Find the decimal of an hour which is second.

A. 0.024            B. 0.00027                C. 0.020                 D. 0.0002

Answer: B. 0.00027

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