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Succeed with maths: part 1
Succeed with maths: part 1

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5 Converting between percentages, decimals and fractions

In the next activity you’ll get some practice in converting between percentages, decimals and fractions. You may wish to do your working out on paper then put your answers in the boxes provided. Show fractions on one line using the ‘/’ symbol, so one half would be entered as ‘1/2’.

Activity 1 Converting between percentages, decimals and fractions

Timing: Allow approximately 10 minutes
  • a.Turn each of these percentages into a decimal and a fraction in its simplest form.
    • i.10%
    • ii.25%
    • iii.50%
    • iv.125%
    • v.0.5%
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Answer

  • a. 

    • i.Decimal: 10% = 0.1 Fraction:  10 percent equation sequence part 1 equals part 2 10 divided by 100 equals part 3 one divided by 10
    • ii.Decimal: 25% = 0.25 Fraction:  25 percent equation sequence part 1 equals part 2 25 divided by 100 equals part 3 one divided by four
    • iii.Decimal: 50% = 0.5 Fraction:  50 percent equation sequence part 1 equals part 2 50 divided by 100 equals part 3 one divided by two
    • iv.Decimal: 125% = 1.25 Fraction:  125 percent equation sequence part 1 equals part 2 125 divided by 100 equals part 3 five divided by four
    • v.Decimal: 0.5% = 0.005 Fraction:  0.5 percent equation sequence part 1 equals part 2 0.5 divided by 100 equals part 3 0.5 multiplication two divided by 100 multiplication two equals part 4 one divided by 200
  • b.Write each of the following fractions and decimals as percentages.
    • i. three divided by four
    • ii. five divided by eight
    • iii. one divided by three
    • iv.0.4
    • v.0.0075

Answer

  • b.Multiplying each fraction or decimal by 100% gives the following answers:
    • i. three divided by four equals three divided by four multiplication 100 percent equals 75 percent
    • ii. five divided by eight equals five divided by eight multiplication 100 percent equals 62.5 percent
    • iii. one divided by three equals one divided by three multiplication 100 percent equals 33 and one divided by three percent
    • iv. 0.4 equals 0.4 multiplication 100 percent equals 40 percent
    • v. 0.0075 equals 0.0075 multiplication 100 percent equals 0.75 percent

By no means did you have to do it this way, but don’t forget that your answer must include a per cent symbol.

Percentages above 100

As you know, 100% means ‘the whole thing’, so what, therefore, do percentages over 100 mean?

Percentages over 100 can be related to top heavy fractions and to decimal numbers bigger than 1. For example, if you wanted to find six divided by five as a percentage, you would do:

equation sequence part 1 six divided by five multiplication 100 percent divided by one equals part 2 600 percent divided by five equals part 3 120 percent

If you wanted to find 1.04 as a percentage, you would shift the decimal point two spaces to the right to get 104%.

But what about in real life? Well, suppose you were earning £20,000 a year and were told you were to get a 5% rise.What you started off with (the £20,000) is your full salary – so 100%. By adding 5% to it your new salary is 105% of the old one.

Now it is time to turn your attention to using percentages and find out how useful these techniques you’ve just covered are.