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 85 17 For example 0.85 = 100 = 20 ÷ 5 hundredths
b On a calculator press: 85 a c 100 =
To change a fraction to a decimal: divide the top by the bottom 4 For example 5 = 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 64 16 or 64% = 100 = 25 b On a calculator press: 64 a c 100 =
To write a decimal or fraction as a %: multiply by 100 For example 0.125 = 0.125 100 = 12.5%
2 2 5 = 5 100 (i.e. of 100%) = 40% or = 2 5 100 = 40%
On a calculator press: 2 5 100 = 40%
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 1 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org 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 1 2 3 10 = ………………. 5 = ………………. 5 = ………………. 4 = …………………
7 2 9 7 8 = ………………. 3 = ………………. 20 =………………. 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 Copiable page 2 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org 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 1 9 3 10 = …………. 5 = …………. 10 = …………. 4 = ………….
4 17 1 2 5 = …………. 20 = …………. 3 = …………. 3 = ………….
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 3 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org 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 Copiable page 4 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org 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 Copiable page 5 of 14 © Nuffield Foundation 2011 ● downloaded from www.fsmq.org 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 Copiable page 6 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – fractions to percentages Set A
I am Who is I am Who is I am Who is
1? 1? 3 ? 100% 2 50% 5 20% 4
I am Who is I am Who is I am Who is
1 ? 1 ? 3 ? 75% 10 10% 4 25% 10
I am Who is I am Who is I am Who is
2 ? 7 ? 4 ? 30% 5 40% 10 70% 5
I am Who is I am Who is I am Who is
3 ? 9 ? 1? 80% 5 60% 10 90%
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 7 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – fractions to percentages Set B
I am Who is I am Who is I am Who is
1? 1? 3 ? 100% 2 50% 5 20% 4
I am Who is I am Who is I am Who is
1 ? 1 ? 3 ? 75% 10 10% 4 25% 10
I am Who is I am Who is I am Who is
2 ? 7 ? 4 ? 30% 5 40% 10 70% 5
I am Who is I am Who is I am Who is
3 ? 9 ? 11? 80% 5 60% 10 90% 20
I am Who is I am Who is I am Who is 3 1 14 55% ? 6% ? 33 1 % ? 50 3 3 25
I am Who is I am Who is I am Who is 5 19 37 56% ? 62 1 % ? 95% ? 8 2 20 50
I am Who is I am Who is I am Who is
3 ? 2 ? 7 ? 74% 8 37 % 25 8% 20
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 8 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am Who is I am Who is I am Who is
2 1 11 35% ? 66 2 % ? 12 1 % ? 3 3 8 2 50
I am Who is I am Who is I am Who is 1 18 7 22% ? 5% ? 72% ? 20 25 8
I am Who is I am Who is I am Who is
1 ? 17 ? 21? 87 % 25 4% 50 34% 50
I am Who is I am Who is I am Who is
13 ? 9 ? 29 ? 42% 25 52% 20 45% 50
I am Who is I am Who is I am Who is
16 ? 8 ? 1 ? 58% 25 64% 25 32% 50
I am Who is I am Who is I am Who is
23 ? 49 ? 11? 2% 25 92% 50 98% 25
I am Who is I am Who is I am Who is
41? 13 ? 7 ? 44% 50 82% 20 65% 50
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 9 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am Who is I am Who is I am Who is
22 ? 31? 17 ? 14% 25 88% 50 62% 20
I am Who is I am Who is I am Who is
4 ? 23 ? 21? 85% 25 16% 50 46% 25
I am Who is I am Who is I am Who is
39 ? 3 ? 13 ? 84% 50 78% 20 15% 50
I am Who is I am Who is I am Who is
6 ? 43 ? 19 ? 26% 25 24% 50 86% 25
I am Who is I am Who is I am Who is
3 ? 9 ? 9 ? 76% 25 12% 50 18% 25
I am Who is I am Who is I am Who is
27 ? 17 ? 1? 36% 50 54% 25 68%
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 10 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – percentages to fractions Set C
I am Who is I am Who is I am Who is
1 1 1 50%? 2 20%? 5 75%?
I am Who is I am Who is I am Who is 3 1 1
4 10%? 10 25% ? 4 30%?
I am Who is I am Who is I am Who is 3 2 7
10 40%? 5 70%? 10 80%?
I am Who is I am Who is I am Who is 4 3 9
5 60%? 5 90%? 10 100%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 11 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – percentages to fractions Set D
I am Who is I am Who is I am Who is
1 1 1 50%? 2 20%? 5 75%?
I am Who is I am Who is I am Who is 3 1 1 4 10%? 10 25%? 4 30%?
I am Who is I am Who is I am Who is 3 2 7 10 40%? 5 70%? 10 80%?
I am Who is I am Who is I am Who is 4 3 9 5 60%? 5 90%? 10 55%?
I am Who is I am Who is I am Who is 11 3 33 20 6%? 50 33%? 100 56%?
I am Who is I am Who is I am Who is 14 63 19 25 63%? 100 95%? 20 74%?
I am Who is I am Who is I am Who is 37 37 2 50 37%? 100 8%? 25 35%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 12 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am Who is I am Who is I am Who is 7 67 13 20 67%? 100 13%? 100 22%?
I am Who is I am Who is I am Who is 11 1 18 50 5%? 20 72%? 25 87%?
I am Who is I am Who is I am Who is 87 1 17 100 4%? 25 34%? 50 42%?
I am Who is I am Who is I am Who is 21 13 9 50 52%? 25 45%? 20 58%?
I am Who is I am Who is I am Who is 29 16 8 50 64%? 25 32%? 25 2%?
I am Who is I am Who is I am Who is 1 23 49 50 92%? 25 98%? 50 44%?
I am Who is I am Who is I am Who is 11 41 13 25 82%? 50 65%? 20 14%?
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 13 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org
I am Who is I am Who is I am Who is 7 22 31 50 88%? 25 62%? 50 85%?
I am Who is I am Who is I am Who is 17 4 23 20 16%? 25 46%? 50 84%?
I am Who is I am Who is I am Who is 21 39 3 25 78%? 50 15%? 20 26%?
I am Who is I am Who is I am Who is 13 6 43 50 24%? 25 86%? 50 76%?
I am Who is I am Who is I am Who is 19 3 9 25 12%? 25 18%? 50 36%?
I am Who is I am Who is I am Who is 9 27 17 100%? 25 54%? 50 68%? 25
Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 14 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org