Information sheet Converting between decimals and fractions To change a decimal to a fraction



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This activity is about converting between fractions, decimals and percentages.

Information sheet

Converting between decimals and fractions

To change a decimal to a fraction: use the place value of the last digit

For example 0.85 = =

On a calculator press: 85 100 =

To change a fraction to a decimal: divide the top by the bottom

For example = 4  5 = 0.8

Converting between percentages and fractions or decimals

To write a % as a fraction or decimal: divide by 100

For example 64% = 64  100 = 0.64

or 64% = =


On a calculator press: 64 100 =


To write a decimal or fraction as a %: multiply by 100

For example 0.125 = 0.125  100 = 12.5%

= 100 (i.e. of 100%) = 40%

or = 2  5  100 = 40%



On a calculator press: 2 5  100 = 40%

Try these

1 Write these decimals as fractions:

0.3 = …………. 0.5 = …………. 0.6 = …………. 0.02 = ………….

0.05 = …………. 0.25 = …………. 0.36 = …………. 0.125 = ………….

2 Write these fractions as decimals:

= ………………. = ………………. = ………………. = …………………

= ………………. = ………………. =………………. = …………………


3 Write these percentages as decimals:

3% = …………. 30% = …………. 25% = …………. 80% = ………….

8% = …………. 12% = …………. 67% = …………. 17.5% = ………….

4 Write these percentages as fractions:

20% = …………. 75% = …………. 5% = …………. 30% = ………….

40% = …………. 15% = …………. 24% = …………. 35% = ………….

5 Write these decimals as percentages:

0.25 = …………. 0.5 = …………. 0.7 = …………. 0.07 = ………….

0.45 = …………. 0.09 = …………. 0.4 = …………. 0.375 = ………….

6 Write these fractions as percentages:

= …………. = …………. = …………. = ………….

= …………. = …………. = …………. = ………….

At the end of the activity

Explain how to convert ...



  • a decimal to a fraction

  • a fraction to a decimal
  • a percentage to a fraction or decimal


  • a fraction or decimal to a percentage.


Give some examples of real contexts where ...

  • decimals are used

  • fractions are used

  • percentages are used.

Fractions to decimals to percentages

Complete this table.


Fraction

Decimal

Percentage

























































































Fill the gaps in the table.

Percentage


Fraction

Decimal

10%











0.2






40%













0.5






70%













0.8






25%














Follow me – fractions to percentages Set A




Follow me – fractions to percentages Set B







Follow me – percentages to fractions Set C



Follow me – percentages to fractions Set D









Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page of

© Nuffield Foundation 2012 ● downloaded from www.fsmq.org






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