Significant Figures - GCSE Maths - Third Space Learning

Example 1: rounding to one significant figure ... Round 3692 to one significant figure 1 s.f. ... The first non-zero digit is the 3 , therefore 3 is the first ... Introduction Whataresignificantfigures? Howtoroundtosignificantfigures Significantfiguresworksheet Roundingtosignificantfigureexamples 1)Roundingtoonesignificantfigure 2)Roundingtotwosignificantfigures 3)Roundingtothreesignificantfigures Commonmisconceptions Relatedlessons Practicesignificantfiguresquestions SignificantfiguresGCSEquestions Learningchecklist Nextlessons Stillstuck? OnetoonemathsinterventionsbuiltforKS4success WeeklyonlineonetooneGCSEmathsrevisionlessonsnowavailable Learnmore InordertoaccessthisIneedtobeconfidentwith: Placevalue Decimals Roundingtothenearest10,100,1000 Decimalplaces Thistopicisrelevantfor: Introduction Whataresignificantfigures? Howtoroundtosignificantfigures Significantfiguresworksheet Roundingtosignificantfigureexamples 1)Roundingtoonesignificantfigure 2)Roundingtotwosignificantfigures 3)Roundingtothreesignificantfigures Commonmisconceptions Relatedlessons Practicesignificantfiguresquestions SignificantfiguresGCSEquestions Learningchecklist Nextlessons Stillstuck? GCSEMaths Number RoundingNumbers SignificantFigures SignificantFigures Herewewilllearnaboutsignificantfiguresincludinghowtoroundnumberstoonesignificantfigure,twosignificantfiguresandthreesignificantfigures. TherearealsoroundingtosignificantfiguresworksheetsbasedonEdexcel,AQAandOCRexamquestions,alongwithfurtherguidanceonwheretogonextifyou’restillstuck. Whataresignificantfigures? Significantfiguresarethedigitsinanumberthatcontributetotheaccuracyofit.Westartcountingsignificantfiguresatthefirstnon-zerodigitofanumberwhichiscalledthefirstsignificantfigure,thenextdigitisthencalledthesecondsignificantfigureandsoon. Asignificantfigurecouldbetotheleftofthedecimalpointortherightofthedecimalpoint. E.g. Roundingnumberstosignificantfigures(oftenabbreviatedtosigfigsors.f.)issimilartoroundingtoanumberofdecimalplaces,units,tens,hundredsandthousandsbutinthiscaseweneedtofindtheappropriatesignificantfiguretogivethecorrectdegreeofaccuracy. Whataresignificantfigures? Howtoroundtosignificantfigures Inordertoroundtoagivennumberofsignificantdigits: Locatethesignificantfigureforthedegreeofaccuracyrequired.Thefirstnon-zerodigitisthefirstsignificantfigure.Lookatthenextdigittotheright.Isit5ormore?Ifitis5ormore–roundupbyadding1tothepreviousdigit.Ifitislessthan5–rounddownbykeepingthepreviousdigitthesame.Ifthedegreeofaccuracyis10ormore,fillinzerostomakethenumberthecorrectsize. Explainhowtoroundtoagivennumberofsignificantdigitsin3steps Significantfiguresworksheet Getyourfreesignificantfiguresworksheetof20+questionsandanswers.Includesreasoningandappliedquestions. DOWNLOADFREE x Significantfiguresworksheet Getyourfreesignificantfiguresworksheetof20+questionsandanswers.Includesreasoningandappliedquestions. DOWNLOADFREE Roundingtosignificantfigureexamples Example1:roundingtoonesignificantfigure Round3692toonesignificantfigure1s.f. Locatethesignificantfigureforthedegreeofaccuracyrequired.Thefirstnon-zerodigitisthefirstsignificantfigure. 3692 Thefirstnon-zerodigitisthe3,therefore3isthefirstsignificantfigure. 2Lookatthenextdigittotheright.Isit5ormore? 3¦692 6ismorethan5. 3Ifitis5ormore–roundupbyadding1tothepreviousdigit.Ifitislessthan5–rounddownbykeepingthepreviousdigitthesame.Ifthedegreeofaccuracyis10ormore,fillinzerostomakethenumberthecorrectsize. As6ismorethan5,weroundup.Adding1tothe3,givesus4.Thefirstsignificantfigurerepresentsthousands,sowemustaddthreezerostomakeitthecorrectsize. 3692is4000to1s.f. Example2:roundingtotwosignificantfigures Round0.07039totwosignificantfigures. Locatethesignificantfigureforthedegreeofaccuracyrequired.Thefirstnon-zerodigitisthefirstsignificantfigure. 0.07039 Thefirstnon-zerodigitisthe7whichisthefirstsignificantfigure,thereforethe0,atthethousandthsplace,isthesecondsignificantfigure. Lookatthenextdigittotheright.Isit5ormore? 0.070¦39 3islessthan5. Ifitis5ormore–roundupbyadding1tothepreviousdigit.Ifitislessthan5–rounddownbykeepingthepreviousdigitthesame.Ifthedegreeofaccuracyis10ormore,fillinzerostomakethenumberthecorrectsize. As3islessthan5,werounddown. 0.07039is0.070to2s.f. Itisimportanttokeepthezeroafterthesevenasitmustbegiventotwosignificantfigures. Example3:roundingtothreesignificantfigures Round24.753tothreesignificantfigures3s.f. Locatethesignificantfigureforthedegreeofaccuracyrequired.Thefirstnon-zerodigitisthefirstsignificantfigure. 24.753 Thefirstnon-zerodigitisthe2whichisthefirstsignificantfigure,thereforethe7,atthetenthsplace,isthethirdsignificantfigure. Lookatthenextdigittotheright.Isit5ormore? 24.7¦53 Thedigittotherightis5. Ifitis5ormore–roundupbyadding1tothepreviousdigit.Ifitislessthan5–rounddownbykeepingthepreviousdigitthesame.Ifthedegreeofaccuracyis10ormore,fillinzerostomakethenumberthecorrectsize. Asitisa5,weroundup. 24.7is24.8to3s.f. Commonmisconceptions Assumingthefirstzerosaresignificant Acommonerroristothinkthefirstzerosinanumberlike0.00467aresignificant.Thesearecalledleadingzerosanddonottellusthesizeofthenumber.Thefirstnon-zerodigitis4,thistellsusthatthenumberisroughly4thousandths. Assumingallzerosarenotsignificant Acommonerroristothinkthatallzerosinanumberlike9006arenotsignificant.Oncethefirstsignificantfigurehasbeenlocated,alldigitsafteraresignificant.Otherwisewemightroundtotheincorrectnumberofsignificantfigures. Leavingoutzerostomakethenumberthecorrectsize Itisimportanttoremembertofillinthezerosifthedegreeofaccuracyismorethan10.Acommonmistakewhenroundinganumberlike378totwosignificantfiguresistosayitis38andnot380. Relatedlessonsonsignificantfigures Significantfiguresarepartofourseriesoflessonstosupportrevisiononroundingnumbers.Youmayfindithelpfultostartwiththemainroundingnumberslessonforasummaryofwhattoexpect,orusethestepbystepguidesbelowforfurtherdetailonindividualtopics.Otherlessonsinthisseriesinclude: RoundingnumbersRoundingtothenearest10,100and1000TruncationEstimation Practicesignificantfiguresquestions Round76340toonesignificantfigure. 8 70000 80000 8000 Thefirstsignificantfigureisthe7.Thenextdigittotherightis6,whichisbiggerthan5,soweroundup.Adding1to7givesus8andfillinginthezerosgivesus80000. 2.Round0.3897toonesignificantfigure. 0.3 0.4 0 1 Thefirstsignificantfigureisthe3.Thenextdigittotherightis8,whichisbiggerthan5,soweroundup.Adding1to3givesus4thereforetheansweris0.4. 3.Round26460totwosignificantfigures. 25000 27000 26 26000 Thefirstsignificantfigureis2andthesecondis6.Thenextnumbertotherightis4,whichislessthan5,sowerounddown.The6remainsthesameandfillinginthezerosgivesus26000. 4.Round78.56totwosignificantfigures. 78.6 78 79 80 Thefirstsignificantfigureis7andthesecondis8.Thenextnumbertotherightis5,soweroundup.Addingonetothe8givesus9andthereforewehave79. 5.Round4.7041294tothreesignificantfigures. 4.70 4.704 4.71 5.70 Thethirdsignificantfigureis0.Thenextfiguretotherightis4,whichislessthan5.Thereforewerounddownandthe0remainsthesame.Theansweris4.70to3s.f. 6.Round0.0051489tothreesignificantfigures. 0.005 0.00515 0.00514 0.00525 Thefirstsignificantfigureis5andthethirdsignificantfigureis4.Thenextnumbertotherightis8,whichisbiggerthan5,soweroundup.Adding1tothe4givesus5andthereforewehave0.00515. SignificantfiguresGCSEquestions 1.(a)Write467983correcttotwosignificantfigures.   (b)Write0.03887correcttoonesignificantfigure.   (c)Write60.7328correcttothreesignificantfigures.   (3marks) Showanswer 470000 (1) 0.04 (1) 60.7 (1) 2.Samwasfindingtheareaofacompoundshape.Hiscalculatedresultwas60942.937cm2.Heneedstoroundthisareatotwosignificantfigures,choosethecorrectanswer.   60900cm2  61000cm2  60942.94cm2  60000cm2   (1mark) Showanswer 61000cm2 3.(a)Useacalculatortoworkout\frac{\sqrt{6.79}}{3.72-2.81}.Writedownallofthedigitsonyourcalculatorscreen.   (b)Roundyouranswertopart(a)tothreesignificantfigures.   (3marks) Showanswer (a)Findingintermediateresultsof2.605…or0.91fromthesubtractionseen. (1) Finalresultof2.863475653 (1) (b)Roundedcorrectlyto2.86 (1) Learningchecklist Youhavenowlearnedhowto: Applyandinterpretlimitsofaccuracywhenrounding Thenextlessonsare DividingdecimalsMultiplyingdecimals Stillstuck? PrepareyourKS4studentsformathsGCSEssuccesswithThirdSpaceLearning.WeeklyonlineonetooneGCSEmathsrevisionlessonsdeliveredbyexpertmathstutors. FindoutmoreaboutourGCSEmathsrevisionprogramme. Introduction Whataresignificantfigures? Howtoroundtosignificantfigures Significantfiguresworksheet Roundingtosignificantfigureexamples 1)Roundingtoonesignificantfigure 2)Roundingtotwosignificantfigures 3)Roundingtothreesignificantfigures Commonmisconceptions Relatedlessons Practicesignificantfiguresquestions SignificantfiguresGCSEquestions Learningchecklist Nextlessons Stillstuck? 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