Lesson 9, Topic 1
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# Fractions – Terminating | Recurring Decimals

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This involves converting fractions to decimal.

There are two types of decimals. These are terminating and recurring decimals.

### 1. Terminating Decimal:

Terminating decimals are obtained when the denominator of a fraction divides the numerate exactly.

### Example 1

Convert the following fractions to decimals:

a. $$\frac{3}{8}$$

b. $$\frac{1}{4}$$

c. $$\frac{2}{5}$$

Solution

a. $$\frac{3}{8}$$

0.375 is a terminating decimal.

b. $$\frac{1}{4}$$

0.25 is a terminating decimal.

c. $$\frac{2}{5}$$

0.4 is a terminating decimal.

### 2. Recurring or Repeating Decimals:

Recurring decimals are obtained when the denominator of a fraction can not divide the numerator exactly. Some digits in a digit repeat infinitely.

### Example 2

Change the following to recurring decimals

a. $$\frac{2}{3}$$

b. $$\frac{5}{7}$$

c. $$\scriptsize 2 \frac{1}{3}$$

Solution

a. $$\frac{2}{3}$$

0.666…….. is a recurring decimal.

b. $$\frac{5}{7}$$

0.71428571….. is a recurring decimal.

c. $$\scriptsize 2 \frac{1}{3}$$

= 0.333

$$\scriptsize 2 \frac{1}{3} \\ \scriptsize = 2 \: + \: 0.33333 \\ \scriptsize = 2.33333…….$$

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