Lesson 7, Topic 4
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# Changing Decimals to Fractions

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Decimal fraction can be expressed as a fraction with a denominator that is a power of ten.

### Example 1

i. Express 0.4 as a fraction
ii. Express 0.37 as a fraction
iii. Express 0.419 as a fraction

Solution

i. Express 0.4 as a fraction

0.4 = $$\frac {4}{10}$$

ii. Express 0.37 as a fraction

0.37 = $$\frac {37}{100}$$

iii. Express 0.419 as a fraction

0.419 = $$\frac {419}{1000}$$

### Example 2

Express 0.625 as a fraction in its lowest terms.

Solution

0.625 = $$\frac {625}{1000} \\ =\frac {625 \div 25}{1000 \div 25} \\ = \frac {25}{40}$$

This is not its lowest term because we can still divide the numerator and denominator by 5

That is, $$\frac {25 \div 5}{40 \div 5}\\ = \frac {5}{8}$$

### Example 3

Express 0.8 as a fraction in its lowest term

Solution

0.8 =  $$\frac {8}{10}\\ = \frac {8 \div 2}{10 \div 2} \\= \frac {4}{5}$$

Hint:
The number of decimal places the given decimal number has, determines the power of ten used to divide.

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