Fractions decimals percentages - Nuffield Foundation
Fractions, decimals and percentages
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
¡Â5
For example
85 = 17
0.85 = 100
20
¡Â5
hundredths
On a calculator press: 85
a b c 100 =
To change a fraction to a decimal: divide the top by the bottom
For example
4 = 4 ? 5 = 0.8
5
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
64 = 16
64% = 100
25
or
On a calculator press: 64 a b c 100 =
To write a decimal or fraction as a %: multiply by 100
For example
0.125 = 0.125 ? 100 = 12.5%
2 = 2 ? 100 (i.e. 2 of 100%) = 40%
5 5
5
or
2 = 2 ? 5 ? 100 = 40%
5
On a calculator press: 2 a b c 5 ? 100 = 40%
Nuffield Free-Standing Mathematics Activity ¡®Fractions, decimals and percentages¡¯ Student sheets
? Nuffield Foundation 2012 ¡ñ downloaded from
Copiable page 1 of 14
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:
7
10 = ¡¡¡¡¡¡.
1 = ¡¡¡¡¡¡.
5
2 = ¡¡¡¡¡¡.
5
3
4 = ¡¡¡¡¡¡¡
7
8 = ¡¡¡¡¡¡.
2 = ¡¡¡¡¡¡.
3
9
20 =¡¡¡¡¡¡.
7
25 = ¡¡¡¡¡¡¡
3 Write these percentages as decimals:
3% = ¡¡¡¡.
30% = ¡¡¡¡.
25% = ¡¡¡¡.
80% = ¡¡¡¡.
8% = ¡¡¡¡.
12% = ¡¡¡¡.
67% = ¡¡¡¡.
17.5% = ¡¡¡¡.
Nuffield Free-Standing Mathematics Activity ¡®Fractions, decimals and percentages¡¯ Student sheets
? Nuffield Foundation 2012 ¡ñ downloaded from
Copiable page 2 of 14
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:
1
10 = ¡¡¡¡.
1 = ¡¡¡¡.
5
9
10 = ¡¡¡¡.
3
4 = ¡¡¡¡.
4 = ¡¡¡¡.
5
17 = ¡¡¡¡.
20
1 = ¡¡¡¡.
3
2 = ¡¡¡¡.
3
Nuffield Free-Standing Mathematics Activity ¡®Fractions, decimals and percentages¡¯ Student sheets
? Nuffield Foundation 2012 ¡ñ downloaded from
Copiable page 3 of 14
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.
Nuffield Free-Standing Mathematics Activity ¡®Fractions, decimals and percentages¡¯ Student sheets
? Nuffield Foundation 2012 ¡ñ downloaded from
Copiable page 4 of 14
Fractions, decimals and percentages
Fractions to decimals to percentages
Complete this table.
Fraction
Decimal
Percentage
1
10
1
5
3
10
2
5
1
2
3
5
7
10
4
5
9
10
1
4
3
4
Nuffield Free-Standing Mathematics Activity ¡®Fractions, decimals and percentages¡¯ Student sheets
? Nuffield Foundation 2011 ¡ñ downloaded from
Copiable page 5 of 14
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