9.1 Converting between percentages, decimals and fractions

Since fractions, decimals and percentages are all just different ways of representing the same thing, we can convert between them in order to compare. Take a look at the video below to see how to convert fractions, decimals and percentages.

Transcript (opens in new window)

Lets look in more detail at changing a percentage to a fraction.

Example: 50% is

As you can see this percentage is essentially a fraction of 100. However you can simplify it to one divided by two.

To change a percentage to a fraction, put the percentage over 100 and simplify if possible.

Sometimes we might see a percentage like this: 12.5%.

If we use the method above we get 12.5 divided by 100 but we can’t have a decimal in a fraction.

To get rid of the decimal in the fraction we must multiply the top and bottom of the fraction, the numerator and denominator, by any number that will give us whole numbers. In this case 10 or 2 both work well (12.5 × 10 = 125 and 12.5 × 2 = 25):

Method 1: × 10

  • 12.5 divided by 100 × top and bottom by 10 = 125 divided by 1000 = one divided by eight

Method 2: × 2

  • 12.5 divided by 100 × top and bottom by 2 = 25 divided by 200 = one divided by eight

Activity 21: Converting between percentages, decimals and fractions

  1. Express these percentages as decimals:

    1. 62%

    2. 50%

    3. 5%

  2. Express these decimals as percentages:

    1. 0.02

    2. 0.2

    3. 0.752

    4. 0.055

  3. Express these percentages as fractions:

    1. 15%

    2. 2.5%

    3. 37.5%

Answer

    1. 0.62

    2. 0.5

    3. 0.05

    1. 2%

    2. 20%

    3. 75.2%

    4. 5.5%

    1. 15 divided by 100 = three divided by 20

       

    2. 2.5 divided by 100 × top and bottom by 10 = 25 divided by 1000 = one divided by 40

       

    3. 37.5 divided by 100 × top and bottom by 10 = 375 divided by 1000 = three divided by eight

       

      You may have multiplied by different numbers to get rid of the decimal in the last two questions. However, your final answers should still be the same as ours.

Now have a go at matching these fractions to decimals and percentages.

Activity 22: Matching fractions, decimals and percentages

Choose the correct fraction for each percentage and decimal.

seven divided by 20

      35% = 0.35 =

italic two divided by italic five

      40% = 0.4 =

two divided by 25

      8% = 0.08 =

five divided by eight

      62.5% = 0.625 =

Using the following two lists, match each numbered item with the correct letter.

  1. seven divided by 20

  2. italic two divided by italic five

  3. two divided by 25

  4. five divided by eight

  1.       35% = 0.35 =

  2.       40% = 0.4 =

  3.       8% = 0.08 =

  4.       62.5% = 0.625 =

The correct answers are:
  • 1 =
  • 2 =
  • 3 =
  • 4 =

Next you’ll look in more detail at how to change a fraction to a percentage.

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