Lesson 2- Writing Decimals as Fractions

Objectives

At the end of this lesson, students should:

• Know the relationship between decimals and fractions
• Be able to write decimals as fractions

From the previous knowledge on fractions, a “whole” can be divided into ten (10) equal parts and each part out of the ten parts is written as. In decimals, is called a tenth and is written as 0.1.

Also, when a whole is divided into hundred equal parts, each part is written as  and is called a hundredth. This is written as 0.01 in the decimal form.

Let’s have a look at the strip below:  

 

The strip has been divided into 10 equal parts. Each part is . This is written as 0.1 in the decimal form.

Having understood this we can view decimals as:

• Tenths, hundredths, thousandths (i.e. 0.1, 0.01 and 0.001)
• A whole number plus tenths, hundredths, thousandths (e.g. 3.5, 8.02, 4.001)

NB: The number of decimal places determines the denominator of the fraction.

• 1 decimal place means a denominator of 10.
• 2 decimal places mean a denominator of 100.
• 3 decimal places mean a denominator of 1000.

Example 1

Write the following decimals as fractions.

1) 0.5                                     2) 0.08                                   3) 0.003

Solution

1) 0.5 =(i.e. 5 out of 10 parts) =

This is because there is only one digit after the decimal point.

2) 0.08 =(i.e. 8 out of 100 parts) =

There are two digits after the decimal point hence a denominator of 100.

3) 0.003 =(i.e. 3 out of 1000 parts)

There are three digits after the decimal point hence a denominator of 1000.

Example 2

Change these decimals to fractions.

a) 1.4             b) 0.35                      c) 2.07                       d) 19.079

Solution

Note that, the digit(s) that come(s) before the decimal point represent(s) the whole number and the digit(s) that come(s) after the decimal point represent(s) the fraction part.

Example 3

Write these decimals as fractions in their simplest form.

a) 0.24                                   b) 3.7                                     c) 248.2