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# Learner Guide

Maths

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Fractions, decimals and percentages

L . O – To be able to convert between fractions, decimals and

percentages.

Fractions, decimals and percentages are all proportions.It is important to be

able to convert between them.

Converting between Fractions and Decimals.

Example

Write 3/5  as a decimal Simply divide 3 by 5.

(use a calculator if you need to) 3÷5 = 0.6.

Converting from decimals to fraction is a tricky one!

This method only works for terminating decimals (recurring decimals will be

looked at later in this topic).

The denominator will be 10, 100, 1000 etc depending on the number of

decimals places.

Example

Write 0.3 as a fraction.

1. Determine the number of decimal places – there is 1 decimal place here.

2. As there is 1 decimal place, the denominator will be 10.

3. The ‘decimal’ given in the question is then written without.

4. The decimal point as the numerator i.e. 0.3 will be written as 3.

5. This fraction cannot be simplified further therefore the answer is 3/10.

 Determine the number of decimal places the number is given toe.g. 0.1 = to 1 dp, 0.35 = 2 dp, 0.657 = 3 dp etcDetermine the denominator of the fractionIf the number is given to 1 dp à denominator is 10If the number is given to 2dp à denominator is 100If the number is given to 3dp à denominator is 1000 etcThe ‘decimal’ given in the question is written without the decimal point as the numerator of the fraction. The denominator is the answer to part 2.Simplify the fraction if possible.

 Convert the following fractions into decimals.1. 1/22. 1/3 3. 1/5 4. 3/10 5. 5/8  Convert the following decimals into fractions. 6. 0.85 7. 0.9 8. 0.125 9. 0.25 10. 0.34  Write all fractions in their simplest form!

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