Significant Figures - Columbia University

1. All non-zero numbers ARE significant. The number 33.2 has THREE significant figures because all of the digits present are non-zero. 2. Zeros ... SignificantFigures Annotationcategory:Chapter5 Note: RULESFORSIGNIFICANTFIGURES 1.Allnon-zeronumbersAREsignificant.Thenumber33.2hasTHREEsignificantfiguresbecauseallofthedigitspresentarenon-zero. 2.Zerosbetweentwonon-zerodigitsAREsignificant.2051hasFOURsignificantfigures.Thezeroisbetweena2anda5. 3.LeadingzerosareNOTsignificant.They'renothingmorethan"placeholders."Thenumber0.54hasonlyTWOsignificantfigures.0.0032alsohasTWOsignificantfigures.Allofthezerosareleading. 4.TrailingzerostotherightofthedecimalAREsignificant.ThereareFOURsignificantfiguresin92.00. 92.00isdifferentfrom92:ascientistwhomeasures92.00millilitersknowshisvaluetothenearest1/100thmilliliter;meanwhilehiscolleaguewhomeasured92millilitersonlyknowshisvaluetothenearest1milliliter.It'simportanttounderstandthat"zero"doesnotmean"nothing."Zerodenotesactualinformation,justlikeanyothernumber.Youcannottagonzerosthataren'tcertaintobelongthere. 5.TrailingzerosinawholenumberwiththedecimalshownAREsignificant.Placingadecimalattheendofanumberisusuallynotdone.Byconvention,however,thisdecimalindicatesasignificantzero.Forexample,"540."indicatesthatthetrailingzeroISsignificant;thereareTHREEsignificantfiguresinthisvalue. 6.TrailingzerosinawholenumberwithnodecimalshownareNOTsignificant.Writingjust"540"indicatesthatthezeroisNOTsignificant,andthereareonlyTWOsignificantfiguresinthisvalue. 7.ExactnumbershaveanINFINITEnumberofsignificantfigures.Thisruleappliestonumbersthataredefinitions.Forexample,1meter=1.00meters=1.0000meters=1.0000000000000000000meters,etc. SonowbacktotheexampleposedintheRoundingTutorial: Round1000.3tofoursignificantfigures. 1000.3hasfivesignificantfigures(thezerosarebetweennon-zerodigits1and3,sobyrule2above,theyaresignificant.)Weneedtodropthefinal3,andsince3<5,weleavethelastzeroalone.so1000.isourfour-significant-figureanswer.(fromrules5and6,weseethatinorderforthetrailingzerosto"count"assignificant,theymustbefollowedbyadecimal.Writingjust"1000"wouldgiveusonlyonesignificantfigure.) 8.Foranumberinscientificnotation:Nx10x,alldigitscomprisingNAREsignificantbythefirst6rules;"10"and"x"areNOTsignificant.5.02x104hasTHREEsignificantfigures:"5.02.""10and"4"arenotsignificant. Rule8providestheopportunitytochangethenumberofsignificantfiguresinavaluebymanipulatingitsform.Forexample,let'strywriting1100withTHREEsignificantfigures.Byrule6,1100hasTWOsignificantfigures;itstwotrailingzerosarenotsignificant.Ifweaddadecimaltotheend,wehave1100.,withFOURsignificantfigures(byrule5.)Butbywritingitinscientificnotation:1.10x103,wecreateaTHREE-significant-figurevalue. Findthistermin:   par# ---- 17