__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

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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