Decimal Fractions

Decimal Fractions

A decimal fraction is a way to represent a fraction where the denominator is a power of 10 (10, 10², 10³, 10⁴, and so on).

Let us look below to understand the difference between decimal fractions and non-decimal fractions.

Example:

Decimal to Fraction

Step 1: Write down the decimal divided by 1, like this: decimal / 1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction.

Example:

Fraction to Decimal

To convert a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number).

For example, if the fraction is 3/4, the decimal would be: 3 ÷ 4 = 0.75

Operations on Decimal Fractions

The four basic operations of mathematics which are addition, subtraction, multiplication and division can be performed on decimal fractions which are discussed below.

Addition of Decimal Fractions

Example: Add 5/100 and 7/100000.

Solution: 5/100 = 0.05
7/10000 = 0.0007

Now, adding the two values we get:
0.05 + 0.0007 = 0.0507

Subtraction of Decimal Fractions

This method is similar to addition.

Example: Subtract 0.0009 and 0.00003.
0.0009 – 0.00003 = 0.00087

Multiplication of Decimal Fractions

Example: Multiply: 0.096 x 100
0.096 x 100 = 9.6

NOTE: When we multiply a decimal fraction by multiples of 10, then we have to shift the decimal point to the right in as many places as the power of 10.

Division of Decimal Fractions

Example: 0.069 ÷ 3
Remove the decimal point from 0.069 and then divide by 3.
69/3 = 23

Now place the decimal point up to three places of decimal.
0.069/3 = 0.023

NOTE: When we divide a decimal fraction by a whole number, then remove the decimal and divide it. Now, place the decimal point as many places as of the dividend.