# Fractions and Decimals

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

Example 1:

 Convert 34 to a decimal number.

 34

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 × 254 × 25

 = 75100

 = 75 ÷ 100

 = 0.75

 The fraction 34 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

 = 0.751.00

Drop the decimal points by multiplying both numerator and denominator by 100.
 = 0.75 × 1001.00 × 100

 = 75100

Simplify either using GCF of 75 and 100 which is 25; or using division by common factors.
 = 75153100204

 = 34

 The decimal number 0.75 is equal to the fraction 34 .

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 + 0.6251.000

Drop the decimal point.
 = 2 + 625125510002008

Simplify either using division by common factors; or using GCF of 625 and 1000 which is 125.
 = 2 + 58
 = 2 58

 The decimal number 2.625 is equal to the fraction 2 58 .