# 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 1 Whole been divided into 10 equal parts. Each part is called

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

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.

Unit 10 Lesson 2: Exercise 1

Convert the following decimals to fractions.

1) 0.9 =       2) 0.11 =

3) 0.7 =       4) 0.09 =

5) 0.78 =       6) 0.48 =

7) 0.83 =       8) 0.22 =

9) 0.120 =       10) 0.850 =

1) 9/10      6) 48/100
2) 11/100      7) 83/100
3) 7/10      8) 22/100
4) 9/100      9) 120/1000
5) 78/100      10) 850/1000

Unit 10 Lesson 2: Exercise 2

Write these decimals as fractions and express them in their lowest terms.

1) 0.04 =        2) 0.97 =

3) 0.5 =        4) 0.255 =

5) 0.23 =        6) 0.49 =

7) 2.5 =        8) 13.24 =

9) 225.14 =        10) 85.860 =

Unit 10 Lesson 2: Exercise 3

Represent these decimals by their simplest fractions.

1) 1.17        2) 6.213

3) 35.35        4) 9.620

5) 12.5        6) 432.8

7) 7.95        8) 15.9

9) 6.07        10) 2.003

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