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Fractions, decimals and percentagesThis activity is about converting between fractions, decimals andpercentages.Information sheetConverting between decimals and fractionsTo change a decimal to a fraction: use the place value of the last digit 5For example85 170.85 10020 5hundredthsOn a calculator press: 85a b c 100 To change a fraction to a decimal: divide the top by the bottomFor example4 4 5 0.85Converting between percentages and fractions or decimalsTo write a % as a fraction or decimal: divide by 100For example 64% 64 100 0.6464 1664% 10025orOn a calculator press: 64 a b c 100 To write a decimal or fraction as a %: multiply by 100For example0.125 0.125 100 12.5%2 2 100 (i.e. 2 of 100%) 40%5 55or2 2 5 100 40%5On 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.orgCopiable page 1 of 14

Try these1 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:710 .1 .52 .534 78 .2 .3920 .725 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.orgCopiable 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:110 .1 .5910 .34 .4 .517 .201 .32 .3Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgCopiable page 3 of 14

At the end of the activityExplain 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.orgCopiable page 4 of 14

Fractions, decimals and percentagesFractions to decimals to percentagesComplete this 9101434Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2011 downloaded from www.fsmq.orgCopiable page 5 of 14

Fill the gaps in the %0.891025%34Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgCopiable page 6 of 14

Follow me – fractions to percentagesI am100%I am75%I am30%I am80%Who is1?2I amWho is1?10I amWho is2?5I amWho is3?5I am50%10%40%60%Set AWho is1?5I amWho is1?4I amWho is7?10I amWho is9?10I amNuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.org20%25%70%90%Who is3?4Who is3?10Who is4?5Who is1?Copiable page 7 of 14

Follow me – fractions to percentagesI am100%I am75%I am30%I am80%I am55%I am56%I am74%Who is1?2I amWho is1?10I amWho is2?5I amWho is3?5I amWho is3 ?50I amWho is5?8I amWho is3?850%10%40%60%6%62 21 %I am37 21 %Set BWho is1?5I amWho is1?4I amWho is7?10I amWho is9?10I amWho is1?3I am20%25%70%90%33 31 %Who is19 ?20I amWho is2 ?25I amNuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.org95%8%Who is3?4Who is3?10Who is4?5Who is11 ?20Who is14 ?25Who is37 ?50Who is7 ?20Copiable page 8 of 14

I am35%I am22%I am87 21 %I am42%I am58%I am2%I am44%Who is2?3I am66 23 %Who is1?20I amWho is1?25I amWho is13 ?25I amWho is16 ?25I amWho is23 ?25I amWho is41 ?50I am5%4%52%64%92%82%Who is1?8I am12 21 %Who is18 ?25I amWho is17 ?50I amWho is9 ?20I amWho is8 ?25I amWho is49 ?50I amWho is13 ?20I amNuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.org72%34%45%32%98%65%Who is11 ?50Who is7?8Who is21 ?50Who is29 ?50Who is1?50Who is11 ?25Who is7 ?50Copiable page 9 of 14

I am14%I am85%I am84%I am26%I am76%I am36%Who is22 ?25I amWho is4?25I amWho is39 ?50I amWho is6 ?25I amWho is3 ?25I amWho is27 ?50I am88%16%78%24%12%54%Who is31 ?50I amWho is23 ?50I amWho is3 ?20I amWho is43 ?50I amWho is9 ?50I amWho is17 ?25I amNuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.org62%46%15%86%18%68%Who is17 ?20Who is21 ?25Who is13 ?50Who is19 ?25Who is9 ?25Who is1?Copiable page 10 of 14

Follow me – percentages to fractionsI am1Who is50%?I am34Who isI am310Who isI am45Who is10%?40%?60%?Set CI am12Who isI am110Who isI am25Who isI am35Who is20%?25% ?70%?90%?Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgI am15Who isI am14Who isI am710Who isI am910Who is75%?30%?80%?100%?Copiable page 11 of 14

Follow me – percentages to fractionsI amWho is150%?I am34Who isI am310Who isI am45Who isI am1120Who isI am1425Who isI am3750Who is10%?40%?60%?6%?63%?37%?Set DI am12Who isI am110Who isI am25Who isI am35Who isI am350Who isI am63100Who isI am37100Who is20%?25%?70%?90%?33%?95%?8%?Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgI am15Who isI am14Who isI am710Who isI am910Who isI am33100Who isI am1920Who isI am225Who is75%?30%?80%?55%?56%?74%?35%?Copiable page 12 of 14

I am720Who isI am1150Who isI am87100Who isI am2150Who isI am2950Who isI am150Who isI am1125Who is67%?5%?4%?52%?64%?92%?82%?I am67100Who isI am120Who isI am125Who isI am1325Who isI am1625Who isI am2325Who isI am4150Who is13%?72%?34%?45%?32%?98%?65%?Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgI am13100Who isI am1825Who isI am1750Who isI am920Who isI am825Who isI am4950Who isI am1320Who is22%?87%?42%?58%?2%?44%?14%?Copiable page 13 of 14

I am750Who isI am1720Who isI am2125Who isI am1350Who isI am1925Who isI am925Who is88%?16%?78%?24%?12%?54%?I am2225Who isI am425Who isI am3950Who isI am625Who isI am325Who isI am2750Who is62%?46%?15%?86%?18%?68%?Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Nuffield Foundation 2012 downloaded from www.fsmq.orgI am3150Who isI am2350Who isI am320Who isI am4350Who isI am950Who isI am1725Who is100%?85%?84%?26%?76%?36%?Copiable page 14 of 14

Fractions, decimals and percentages Nuffield Free-Standing Mathematics Activity ZFractions, decimals a