Significant Figures Calculator - Sig Fig

When dealing with estimation, the number of significant digits should be no more than the log base 10 of the sample size and rounding to the ... OmniCalculatorlogoWe’rehiring!EmbedShareviaSignificantFiguresCalculator-SigFigByDanielTrojanowskiandStevenWoodingLastupdated:Dec09,2021Tableofcontents:Whataresignificantfigures?Whatarethesignificantfiguresrules?HowtousethesigfigcalculatorSignificantfiguresinoperationsFAQThesignificantfigurescalculatorconvertsanynumberintoanewnumberwiththedesiredamountofsigfigsANDsolvesexpressionswithsigfigs(trydoing3.14/7.58-3.15).Whatarethesignificantfiguresrules?Thoseconceptswillbeexplainedthroughoutthispageaswellashowtouseasigfigcalculator. Whataresignificantfigures? Significantfiguresareallnumbersthataddtothemeaningoftheoverallvalueofthenumber.Topreventrepeatingfiguresthataren'tsignificant,numbersareoftenrounded.Onemustbecarefulnottoloseprecisionwhenrounding.Manytimesthegoalofroundingnumbersisjusttosimplifythem.Usetheroundingcalculatortoassistwithsuchproblems. Whatarethesignificantfiguresrules? Todeterminewhatnumbersaresignificantandwhicharen't,usethefollowingrules: Thezerototheleftofadecimalvaluelessthan1isnotsignificant. Alltrailingzerosthatareplaceholdersarenotsignificant. Zerosbetweennon-zeronumbersaresignificant. Allnon-zeronumbersaresignificant. Ifanumberhasmorenumbersthanthedesirednumberofsignificantdigits,thenumberisrounded.Forexample,432,500is433,000to3significantdigits(usinghalfup(regular)rounding). Zerosattheendofnumberswhicharenotsignificantbutarenotremoved,asremovingwouldaffectthevalueofthenumber.Intheaboveexample,wecannotremove000in433,000unlesschangingthenumberintoscientificnotation. Howtousethesigfigcalculator Oursignificantfigurescalculatorworksintwomodes-itperformsarithmeticoperationsonmultiplenumbers(forexample,4.18/2.33)orsimplyroundsanumbertoyourdesirednumberofsigfigs. Followingtherulesnotedabove,wecancalculatesigfigsbyhandorbyusingthesignificantfigurescounter.Supposewehavethenumber0.004562andwant2significantfigures.Thetrailingzerosareplaceholders,sowedonotcountthem.Next,weround4562to2digits,leavinguswith0.0046. Nowwe'llconsideranexamplethatisnotadecimal.Supposewewant3,453,528to4significantfigures.Wesimplyroundtheentirenumbertothenearestthousand,givingus3,454,000. Whatifanumberisinscientificnotation?Insuchcasesthesamerulesapply.Toenterscientificnotationintothesigfigcalculator,useEnotation,whichreplacesx10witheitheraloweroruppercaseletter'e'.Forexample,thenumber5.033x10^^23^^isequivalentto5.033E23(or5.033e23).Foraverysmallnumbersuchas6.674x10^^-11^^theEnotationrepresentationis6.674E-11(or6.674e-11). Whendealingwithestimation,thenumberofsignificantdigitsshouldbenomorethanthelogbase10ofthesamplesizeandroundingtothenearestinteger.Forexample,ifthesamplesizeis150,thelogof150isapproximately2.18,soweuse2significantfigures. Significantfiguresinoperations Thereareadditionalrulesregardingtheoperations-addition,subtraction,multiplication,anddivision. Foradditionandsubtractionoperations,theresultshouldhavenomoredecimalplacesthanthenumberintheoperationwiththeleastprecision.Forexample,whenperformingtheoperation128.1+1.72+0.457,thevaluewiththeleastnumberofdecimalplaces(1)is128.1.Hence,theresultmusthaveonedecimalplaceaswell:128.̲1+1.7̲2+0.45̲7=130.̲277=130.̲3.Thepositionofthelastsignificantnumberisindicatedbyunderliningit. Formultiplicationanddivisionoperations,theresultshouldhavenomoresignificantfiguresthanthenumberintheoperationwiththeleastnumberofsignificantfigures.Forexample,whenperformingtheoperation4.321*3.14,thevaluewiththeleastsignificantfigures(3)is3.14.Sotheresultmustalsobegiventothreesignificantfigures:4.32̲1*3.1̲4=13.̲56974=13.̲6. Ifperformingadditionandsubtractiononly,itissufficienttodoallcalculationsatonceandapplythesignificantfiguresrulestothefinalresult. Ifperformingmultiplicationanddivisiononly,itissufficienttodoallcalculationsatonceandapplythesignificantfiguresrulestothefinalresult. If,however,youdomixedcalculations-addition/subtractionandmultiplication/division-youneedtonotethenumberofsignificantfiguresforeachstepofthecalculation.Forexample,forthecalculation12.1̲3+1.7̲2*3.̲4,afterthefirststep,youwillobtainthefollowingresult:12.1̲3+5.̲848.Now,notethattheresultofthemultiplicationoperationisaccurateto2significantfigures,andmoreimportantly,onedecimalplace.Youshouldn'troundtheintermediateresultandonlyapplythesignificantdigitrulestothefinalresult.Soforthisexample,thefinalstepsofthecalculationare12.1̲3+5.̲848=17.̲978=18.̲0. Exactvalues,includingdefinednumberssuchasconversionfactorsand'pure'numbers,don'taffecttheaccuracyofthecalculation.Theycanbetreatedasiftheyhadaninfinitenumberofsignificantfigures.Forexample,whenusingthespeedconversion,youneedtomultiplythevalueinm/sby3.6ifyouwanttoobtainthevalueinkm/h.Thenumberofsignificantfiguresisstilldeterminedbytheaccuracyoftheinitialspeedvalueinm/s-forexample,15.23*3.6=54.83. Touseanexactvalueinthecalculator,givethevaluetothegreatestnumberofsignificantfiguresinthecalculation.Soforthisexample,youwouldenter15.23*3.600intothecalculator. Sincewearetalkingaboutbasicarithmeticoperations,howaboutcheckingourdistributivepropertycalculatortolearnhowtohandlecomplexmathematicalproblemsthatinvolvemorethanonearithmeticoperation? FAQ Howmanysigfigsin100? 100hasonesignificantfigure(andit'sanumber1).Why?Becausetrailingzerosdonotcountassigfigsifthere'snodecimalpoint. Howmanysigfigsin100.00? 100.00hasfivesignificantfigures(andit'sanumber1).Thisisbecausetrailingzerosdocountassigfigsifthedecimalpointispresent. Howmanysigfigsin0.01? 0.01hasonesignificantfigure(andit'sanumber1).Why?Becauseleadingzerosdonotcountassigfigs. Howmanysignificantfiguresinthemeasurementof0.00208gram? 0.00208hasthreesignificantfigures(2,0,and8).Why?Becauseleadingzerosdonotcountassigfigs,butzeroessandwichedbetweennon-zerofiguresdocount. Howmanysignificantfiguresinthemeasurementof100.10in? 100.10hasfivesignificantfigures,thatis,allitsfiguresaresignificant.Why?Becausethezeroessandwichedbetweennon-zerofiguresalwayscountassigfigs,andthereisthedecimaldot,sothetrailingzeroscountaswell. Whatis2648tothreesignificantfigures? 2648tothreesignificantfiguresis2650. Whatis2648totwosignificantfigures? 2648totwosignificantfiguresis2600. DanielTrojanowskiandStevenWoodingEnternumberorexpression(e.g."5.13*3.78")NumberorexpressionRoundtosigfig(optional)AdvancedmodeCheckout321similarmathcalculators306090triangle454590triangleAbsolutevalue…318moreBlackHoleCollisionCalculatorTheBlackHoleCollisionCalculatorletsyouseetheeffectsofablackholecollision,aswellasrevealingsomeofthemysteriesofblackholes,comeoninandenjoy!BlackHoleCollisionCalculatorCarcrashforceWiththiscarcrashcalculator,youcanfindouthowdangerousarecarcrashes.CarCrashCalculatorMeatfootprintCheckoutthemeatimpact-ontheenvironmentandyourhealth.MeatFootprintCalculatorSchwarzschildradiusCalculatethegravitationalaccelerationattheeventhorizonofablackholeofagivenmassusingtheSchwarzschildradiuscalculator.SchwarzschildRadiusCalculator