Fractions and Decimals


Fractions and decimals are related to each other. Let's see how.


Example 1:

   Convert  3
4
  to a decimal number.

   

    3
4

Change the fraction to a decimal fraction.

A decimal fraction is a fraction in which the denominator is a number related to 10.

Example: 10, 100, 1000, 10000; it's basically 1 followed by any number of zeroes.
 = 3 × 25
4 × 25

 =  75
100

 = 75 ÷ 100

 = 0.75


The fraction  3
4
  is equal to the decimal number 0.75.


Example 2:

   Change 0.75 to a fraction.

   

    0.75

Since there are 2 places after the decimal point in the numerator, we put 2 zeroes after the decimal point in the denominator.
 = 0.75
  1

 = 0.75
1.00

Drop the decimal points by multiplying both numerator and denominator by 100.
 = 0.75 × 100
1.00 × 100

 =  75
100

Simplify either using GCF of 75 and 100 which is 25; or using division by common factors.
 = 75153
100204

 = 3
4

The decimal number 0.75 is equal to the fraction  3
4
  .


Example 3:

   Change 2.625 to a fraction.

Split the number into its whole number part and the decimal part.
    2.625

 = 2 + 0.625

 = 2 +  0.625
1.000

Drop the decimal point.
 = 2 +   6251255
10002008

Simplify either using division by common factors; or using GCF of 625 and 1000 which is 125.
 = 2 +  5
8
 = 5
8

The decimal number 2.625 is equal to the fraction 2 5
8
  .