__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: **

**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

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