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
÷5
For example
85 = 17
0.85 = 100
20
÷5
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 ● downloaded from www.fsmq.org
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 ● downloaded from www.fsmq.org
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 ● downloaded from www.fsmq.org
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 ● downloaded from www.fsmq.org
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 ● downloaded from www.fsmq.org
Copiable page 5 of 14
Fill the gaps in the table.
Percentage
Fraction
Decimal
10%
0.2
3
10
40%
0.5
3
5
70%
0.8
9
10
25%
3
4
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
Copiable page 6 of 14
Follow me – fractions to percentages
I am
100%
I am
75%
I am
30%
I am
80%
Who is
1?
2
I am
Who is
1?
10
I am
Who is
2?
5
I am
Who is
3?
5
I am
50%
10%
40%
60%
Set A
Who is
1?
5
I am
Who is
1?
4
I am
Who is
7?
10
I am
Who is
9?
10
I am
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
20%
25%
70%
90%
Who is
3?
4
Who is
3?
10
Who is
4?
5
Who is
1?
Copiable page 7 of 14
Follow me – fractions to percentages
I am
100%
I am
75%
I am
30%
I am
80%
I am
55%
I am
56%
I am
74%
Who is
1?
2
I am
Who is
1?
10
I am
Who is
2?
5
I am
Who is
3?
5
I am
Who is
3 ?
50
I am
Who is
5?
8
I am
Who is
3?
8
50%
10%
40%
60%
6%
62 21 %
I am
37 21 %
Set B
Who is
1?
5
I am
Who is
1?
4
I am
Who is
7?
10
I am
Who is
9?
10
I am
Who is
1?
3
I am
20%
25%
70%
90%
33 31 %
Who is
19 ?
20
I am
Who is
2 ?
25
I am
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
95%
8%
Who is
3?
4
Who is
3?
10
Who is
4?
5
Who is
11 ?
20
Who is
14 ?
25
Who is
37 ?
50
Who is
7 ?
20
Copiable page 8 of 14
I am
35%
I am
22%
I am
87 21 %
I am
42%
I am
58%
I am
2%
I am
44%
Who is
2?
3
I am
66 23 %
Who is
1?
20
I am
Who is
1?
25
I am
Who is
13 ?
25
I am
Who is
16 ?
25
I am
Who is
23 ?
25
I am
Who is
41 ?
50
I am
5%
4%
52%
64%
92%
82%
Who is
1?
8
I am
12 21 %
Who is
18 ?
25
I am
Who is
17 ?
50
I am
Who is
9 ?
20
I am
Who is
8 ?
25
I am
Who is
49 ?
50
I am
Who is
13 ?
20
I am
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
72%
34%
45%
32%
98%
65%
Who is
11 ?
50
Who is
7?
8
Who is
21 ?
50
Who is
29 ?
50
Who is
1?
50
Who is
11 ?
25
Who is
7 ?
50
Copiable page 9 of 14
I am
14%
I am
85%
I am
84%
I am
26%
I am
76%
I am
36%
Who is
22 ?
25
I am
Who is
4?
25
I am
Who is
39 ?
50
I am
Who is
6 ?
25
I am
Who is
3 ?
25
I am
Who is
27 ?
50
I am
88%
16%
78%
24%
12%
54%
Who is
31 ?
50
I am
Who is
23 ?
50
I am
Who is
3 ?
20
I am
Who is
43 ?
50
I am
Who is
9 ?
50
I am
Who is
17 ?
25
I am
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
62%
46%
15%
86%
18%
68%
Who is
17 ?
20
Who is
21 ?
25
Who is
13 ?
50
Who is
19 ?
25
Who is
9 ?
25
Who is
1?
Copiable page 10 of 14
Follow me – percentages to fractions
I am
1
Who is
50%?
I am
3
4
Who is
I am
3
10
Who is
I am
4
5
Who is
10%?
40%?
60%?
Set C
I am
1
2
Who is
I am
1
10
Who is
I am
2
5
Who is
I am
3
5
Who is
20%?
25% ?
70%?
90%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am
1
5
Who is
I am
1
4
Who is
I am
7
10
Who is
I am
9
10
Who is
75%?
30%?
80%?
100%?
Copiable page 11 of 14
Follow me – percentages to fractions
I am
Who is
1
50%?
I am
3
4
Who is
I am
3
10
Who is
I am
4
5
Who is
I am
11
20
Who is
I am
14
25
Who is
I am
37
50
Who is
10%?
40%?
60%?
6%?
63%?
37%?
Set D
I am
1
2
Who is
I am
1
10
Who is
I am
2
5
Who is
I am
3
5
Who is
I am
3
50
Who is
I am
63
100
Who is
I am
37
100
Who is
20%?
25%?
70%?
90%?
33%?
95%?
8%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am
1
5
Who is
I am
1
4
Who is
I am
7
10
Who is
I am
9
10
Who is
I am
33
100
Who is
I am
19
20
Who is
I am
2
25
Who is
75%?
30%?
80%?
55%?
56%?
74%?
35%?
Copiable page 12 of 14
I am
7
20
Who is
I am
11
50
Who is
I am
87
100
Who is
I am
21
50
Who is
I am
29
50
Who is
I am
1
50
Who is
I am
11
25
Who is
67%?
5%?
4%?
52%?
64%?
92%?
82%?
I am
67
100
Who is
I am
1
20
Who is
I am
1
25
Who is
I am
13
25
Who is
I am
16
25
Who is
I am
23
25
Who is
I am
41
50
Who is
13%?
72%?
34%?
45%?
32%?
98%?
65%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am
13
100
Who is
I am
18
25
Who is
I am
17
50
Who is
I am
9
20
Who is
I am
8
25
Who is
I am
49
50
Who is
I am
13
20
Who is
22%?
87%?
42%?
58%?
2%?
44%?
14%?
Copiable page 13 of 14
I am
7
50
Who is
I am
17
20
Who is
I am
21
25
Who is
I am
13
50
Who is
I am
19
25
Who is
I am
9
25
Who is
88%?
16%?
78%?
24%?
12%?
54%?
I am
22
25
Who is
I am
4
25
Who is
I am
39
50
Who is
I am
6
25
Who is
I am
3
25
Who is
I am
27
50
Who is
62%?
46%?
15%?
86%?
18%?
68%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets
© Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am
31
50
Who is
I am
23
50
Who is
I am
3
20
Who is
I am
43
50
Who is
I am
9
50
Who is
I am
17
25
Who is
100%?
85%?
84%?
26%?
76%?
36%?
Copiable page 14 of 14