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# Fractions, decimals and percentages

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Maths

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Converting between Fractions and Percentages

In order to convert between fractions and percentages you will first need to

convert to decimals!

Example

Write 1/5  as a percentage

1. First, you need to convert this fraction into a decimal → 0.2
2. Then, convert the decimal into a percentage → 20%

Example

Write 65% as a fraction

1. First, you need to convert this percentage into a decimal → 65
2. Then, convert the decimal into a fraction → 65/100

 Convert the following fractions into percentages.1. 2/52. 8/103. 2/54. 3/45. 4/15 Convert the percentages into fractions.6. 80%7. 45%8. 100&9. 43.5%10. 34%

Recurring Decimals

Terminating decimals are finite e.g

Recurring decimals have a pattern of numbers which repeats continuously

Converting Recurring Decimals into Fractions

The fraction will have the ‘repeating unit’ of the pattern of the decimal as the

numerator. The denominator will be the same number of 9’s as there are

numbers in the repeating unit.

Example

Write the recurring decimal 0.666666.. as a fraction

1. The repeating unit is ‘6’ → this will be the numerator of the fraction
1. The denominator will be 9
1. The fraction is 6/9

 StepsDetermine the repeating unit of the decimal. e.g. the repeating unit of 0.4444… = 40.65656565… = 650.123123123… = 123This repeating unit will be the numerator of the fraction The denominator is then the same number of 9s as there are numbers in the repeating unit. e.g. if the repeating unit is 4 à denominator will be 965 à denominator will be 99123 à denominator will be 999 Write out the fraction and simplify it if possible.

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