Fraction and Decimals

A decimal number system is used to express the whole number and fraction together. Here, we will separate the whole number from the fraction by inserting a ".", which is called a decimal point. And a fraction represents a value in the form of a/b. There is a close relationship between decimals and fractions. To convert any decimal number to a fraction, we ignore the decimal point and divide the number by the place value of the last digit in the fractional part of the number. Then we simplify the fraction so obtained. The decimals and fractions can be conveniently interchanged to each other.

Decimal Fractions

Decimal fractions Math is the representation of the decimal form of fractions, whose denominator is 10 or higher powers of 10, like 100, 1000, 10000, etc. For example 1/10, 1/100, 1/1000, are fractions in decimal. If we simplify such fractions, we can write them in the decimal form such as 0.1, 0.01, 0.001, etc. It is easy to solve mathematical problems that are represented in the form of decimal fractions, such as dividing fractions, multiplying fractions, etc.

A fraction represents a part of the whole. For example, it tells how many slices of a pizza left or eaten with respect to the whole pizza-like, one-half, three-quarters. Generally, a fraction has two parts i.e. the numerator and the denominator. A decimal fraction is a fraction where its denominator is a power of 10 i.e. 101,102, 103 etc.

Conversion to Decimal Fractions

1. Conversion from fractions to decimal fractions

  • Let us consider an example of a fraction, 3/2. 
  • The first step would be to consider the number that gives 10 or a multiple of 10 when multiplied by the denominator. In this case, 5 multiplied by 2 gives 10. 
  • Now multiply the numerator and denominator with the same number to get your decimal fraction. Here, 3 x 5/ 2 x 5 gives 15/10. 
  • Thus, the decimal fraction of 3/2 is 15/10. 

2. Conversion from mixed numbers to decimal fractions

  • Convert the mixed fraction into a normal fraction.
  • Follow the steps for converting fractions to decimal fractions. 

3. Conversion from decimal numbers to decimal fractions

  • Write the original decimal number in the numerator and denominator form by placing 1 in the denominator: 4.3/1.
  • For every space that you move the decimal point, add a zero next to the 1 in the denominator: 43/10 (As we can see one shift of decimal space, one 0 must be added to the denominator). 



  • Once the number in the numerator is non-decimal, you have got your decimal fraction: 4.3 = 43/10.

Real-Life Application of Decimal Fractions

Decimal fractions are used for understanding precise quantities instead of whole numbers. You will also use them for expressing percentages. For instance, 97% can be written as 97/100 for ease of calculation.