Significant Figures | Introduction to Chemistry - Lumen Learning

Zeros appearing between two non-zero digits (trapped zeros) are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1, and 2. Leading zeros ( ... Skiptomaincontent IntroductiontoChemistry IntroductiontoChemistry Searchfor: SignificantFigures   LearningObjective Applyknowledgeofsignificantfigurestoscientificcalculations KeyPoints Significantfiguresareanynon-zerodigitsortrappedzeros.Theydonotincludeleadingortrailingzeros. Whengoingbetweendecimalandscientificnotation,maintainthesamenumberofsignificantfigures. Thefinalanswerinamultiplicationordivisionproblemshouldcontainthesamenumberofsignificantfiguresastheoriginalnumberwiththefewestsignificantfigures. Inadditionandsubtraction,thefinalanswershouldcontainthesamenumberofdecimalplacesastheoriginalnumberwiththefewestnumberofdecimalplaces. Term SignificantFiguresThedigitsthatcarrymeaninginanumberandcontributetoitsprecision. Significantfiguresofanumberaredigitswhichcontributetotheprecisionofthatnumber.Numbersthatdonotcontributeanyprecisionandshouldnotbecountedasasignificantnumberare: leadingortrailingzeros(thoseareplaceholders) digitsthatareintroducedbycalculationsthatgivethenumbermoreprecisionthantheoriginaldataallows. PiThiscalculatorshowseightsignificantfiguresofpi. RulesForDeterminingIfaNumberIsSignificantorNot Allnon-zerodigitsareconsideredsignificant.Forexample,91hastwosignificantfigures(9and1),while123.45hasfivesignificantfigures(1,2,3,4,and5). Zerosappearingbetweentwonon-zerodigits(trappedzeros)aresignificant.Example:101.12hasfivesignificantfigures:1,0,1,1,and2. Leadingzeros(zerosbeforenon-zeronumbers)arenotsignificant.Forexample,0.00052hastwosignificantfigures:5and2. Trailingzeros(zerosafternon-zeronumbers)inanumberwithoutadecimalaregenerallynotsignificant(seebelowformoredetails).Forexample,400hasonlyonesignificantfigure(4).Thetrailingzerosdonotcountassignificant. Trailingzerosinanumbercontainingadecimalpointaresignificant.Forexample,12.2300hassixsignificantfigures:1,2,2,3,0,and0.Thenumber0.000122300stillhasonlysixsignificantfigures(thezerosbeforethe1arenotsignificant).Inaddition,120.00hasfivesignificantfiguressinceithasthreetrailingzeros.Thisconventionclarifiestheprecisionofsuchnumbers.Forexample,ifameasurementthatisprecisetofourdecimalplaces(0.0001)isgivenas12.23,thenthemeasurementmightbeunderstoodashavingonlytwodecimalplacesofprecisionavailable.Statingtheresultas12.2300makesitclearthatthemeasurementisprecisetofourdecimalplaces(inthiscase,sixsignificantfigures). Thenumber0hasonesignificantfigure.Therefore,anyzerosafterthedecimalpointarealsosignificant.Example:0.00hasthreesignificantfigures. Anynumbersinscientificnotationareconsideredsignificant.Forexample,4.300x10-4has4significantfigures. ConventionsAddressingSignificantFigures Thesignificanceoftrailingzerosinanumbernotcontainingadecimalpointcanbeambiguous.Forexample,itmaynotalwaysbeclearifanumberlike1300isprecisetothenearestunit(andjusthappenscoincidentallytobeanexactmultipleofahundred)orifitisonlyshowntothenearesthundredduetoroundingoruncertainty.Variousconventionsexisttoaddressthisissue: Abarmaybeplacedoverthelastsignificantfigure,showingthatanytrailingzerosfollowingthisareinsignificant.Forexample,1300withabarplacedoverthefirst0wouldhavethreesignificantfigures(withthebarindicatingthatthenumberisprecisetothenearestten). Thelastsignificantfigureofanumbermaybeunderlined;forexample,“2000”hastwosignificantfigures. Adecimalpointmaybeplacedafterthenumber.Forexample“100.”indicatesspecificallythatthreesignificantfiguresaremeant. Inthecombinationofanumberandaunitofmeasurementtheambiguitycanbeavoidedbychoosingasuitableunitprefix.Forexample,thenumberofsignificantfiguresinamassspecifiedas1300gisambiguous,whileinamassof13hgor1.3kg,itismuchclearer. Whenconvertingfromdecimalformtoscientificnotation,alwaysmaintainthesamenumberofsignificantfigures.Forexample,0.00012hastwosignificantfigures,thereforethecorrectscientificnotationforthisnumberwouldbe1.2x10-4. Whenmultiplyinganddividingnumbers,thenumberofsignificantfiguresusedisdeterminedbytheoriginalnumberwiththesmallestamountofsignificantfigures.Whenaddingandsubtracting,thefinalnumbershouldberoundedtothedecimalpointoftheleastprecisenumber. Examples: 1.423x4.2=6.0since1.423has4significantfiguresand4.2onlyhastwosignificantfigures,thefinalanswermustalsohave2significantfigures. 234.67–43.5=191.2since43.5hasonedecimalplaceand234.67hastwodecimalplaces,thefinalanswermusthavejustonedecimalplace. AnotherWaytoDetermineSigFigs:ThePacificRule&theAtlanticRule Itcanbechallengingtorememberalltherulesaboutsignificantfiguresandwhethereachzeroissignificantornotsignificant.Here’sanotherwaytodeterminesignificantfigures(sigfigs):thePacificandAtlanticRule. IfanumberhasadecimalPresent,usethePacificrule(notethedoubleP’s).ThePacificOceanisontheleftsideoftheUnitedStatessostartattheleftsideofthenumber.Startcountingsigfigsatthefirstnon-zeronumberandcontinuetotheendofthenumber.Forexample,sincethereisadecimalpresentin0.000560startfromtheleftsideofthenumber.Don’tstartcountingsigfigsuntilthefirstnon-zeronumber(5),thencountallthewaytotheendofthenumber.Therefore,thereare3sigfigsinthisnumber(5,6,0). Ifanumberhasnodecimal(thedecimalisAbsent)usetheAtlanticrule(again,notethedoubleA’s).SincetheAtlanticOceanisontherightsideoftheUnitedStates,startontherightsideofthenumberandstartcountingsigfigsatthefirstnon-zeronumber.Forexample,sincethereisnodecimalin2900startfromtherightsideofthenumberandstartcountingsigfigsatthefirstnonzeronumber(9).Sotherearetwosigfigsinthisnumber(2,9). SignificantFiguresMadeEasy!–YouTubeDon’tbeconfusedbysignificantfigures.Itwilljustmakesensewiththisvideo.Thevideointroducessignificantfiguresanddiscusseshowtoroundformultiplicationanddivisionusingsignificantfigures. 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