Significant Figures - Definition, Rules, Rounding ... - Cuemath

For example, 0.0012 contained two significant digits. If zeros are placed on the right of the decimal and not have a non-zero digit after that, then it is ... LearnPracticeDownload SignificantFigures Significantfiguresarealsocalled significantdigits,astheyareestablishedintheformofdigits.Thenumberofsignificantdigitscanbeidentifiedbycountingallthevaluesstarting fromthe1stnon-zerodigitlocatedontheleft.Thesenumbersarereliable and necessarytoindicatethequantityofalength,volume,mass,measurement,andsoon.Arithmeticoperationssuchasaddition,subtraction,multiplication,anddivisionareusedwhilecalculatingsignificantfigures. 1. WhatareSignificantFigures? 2. RulesofSignificantFigures 3. RoundingSignificantFigures  4. SolvedExamplesonSignificantFigures 5. PracticeQuestions 6. FAQsonSignificantFigures WhatareSignificantFigures?  SignificantFiguresrefertothenumberofimportantsingledigitsfrom0to9inthecoefficientoftheexpressionthatconveysthemessageaccurately.Thesesignificantfigureshelpengineersorscientistsinassertingthequantityofanymeasurement,length,volume,ormass.Forexample,453hasthreesignificantfigures.  Thetwomainapplicationstounderstandsignificantfiguresare-PrecisionandAccuracy.Let'slearnhowthesetwotermsplayanimportantroleinreal-lifesituationswhenitcomestotheconceptofsignificantfigures.   Precision-Theclosenessbetweentwoormorequantitiestoeachotherunderthesameconditioniscalledprecision.Inprecision,thelevelofmeasurementwhenrepeatedgivesthesameresultandtheindividualmeasurementagreestoeachother.  Accuracy-Theclosenessbetweenthemeasurementandtheaccuratenumberiscalledaccuracy.Accuracyhelpsinprovidingconsistentresultswithnoerroralongwithaccuracyintheresult.  RulesofSignificantFigures Tomeasurethesignificantfiguresofacalculatedmeasurement,therearecertainrulesthatneedtobefollowedandremembered.  Allthedigitsexceptzeroarealwayssignificant.Forexample,894621 containssixsignificantdigits. Anyzerosplacedinbetweenanytwonon-zerodigitsaresignificant.Forexample,10.007containsfive significantdigits. Ifzerosareplacedbothontherightofadecimalpointandleftofanon-zerodigit,theyarenotsignificant. Forexample,0.0012containedtwo significantdigits. Ifzerosareplacedontherightofthedecimalandnothaveanon-zerodigitafterthat,thenitissignificant. Forexample,80.00containsfoursignificantdigits. Zerosplacedontherightofthelastnon-zerodigitafterthedecimalpointaresignificant. Forexample,0.00153100containssixsignificantdigits. Zerosthatareplacedontherightofthelastnon-zerodigitaresignificantwhentheycomefromameasurement.Forexample,3560 mcontainsfoursignificantdigits.  Inthefiguregivenbelow,thereare4significantdigitsinthenumber0.00003400 RoundingSignificantFigures Roundingsignificantfiguresisdonebyconsideringthefirstnon-zerodigitifweareroundingoffuptoonesignificantfigure.Lookatthenextdigittotheright,ifitequalstoorgreaterthan5,thenadd1tothefirstnon-zerodigit,ifitislessthan5deduct1fromthefirstnon-zerodigit. RoundingSignificantnumbershavetwomainrules: Identifythedigittoberoundedoff.Ifafterroundingoffthenumber,thenumberislessthan5thenallthenumberspresentontherightsideneedstobeexcluded.  Oncetherounded-offdigitisgreaterthan5thenthenumber1needstobeaddedtotherounding-offdigitandexcludetheothernumbersontherightside.  Forexample,0.05491ifwehavetoroundthisnumbertoathree-digitsignificantfigure,firstcheckthelastdigit.Inthiscase,thelastdigitis1whichislesser than5,soitwon'troundupsincethesenumbersareafterthedecimalpoint.Hence,thenumberwillroundupto0.0549.Furtherroundittotwo-digit,itwillbe0.055since9isgreaterthan5andisdroppedtomakethenumber4into5. TopicsRelatedtoSignificantFigures Checkouttheseinterestingarticlestoknowmoresignificantfiguresanditsrelatedarticles. RoundingNumbers  Measurement  Decimal  Whatarenumbers? WholeNumbers Fractions   Example1:Writedownthesignificantfiguresofthelistofnumbers367,0.0075,56.004,98.70,and230.00  Solution:Fromthelistofnumbers,letusfindoutthesignificantfiguresofeachnumber.  367-Threesignificantfigures  0.0075-Twosignificantfigures 56.004-Fivesignificantfigures  98.70-Foursignificantfigures 230.00-Fivesignificantfigures Example2:Findthesignificantfiguresfromthesumofthesenumbers67+12.6+3.40+22  Solution:First,weneedtoaddthelistofnumberstofindthetotalsum.  67+12.6+3.40+22=105 Therefore,thesignificantdigitsarethreewhichare1,0,and5. Example3:Roundoffthelistofnumbers34.05,21.3,76.9,44.7totwosignificantfigures. Solution:Keepingtheroundingoffrulesinmind,letusroundoffeverynumberonebyone.  34.05~34 21.3~21 76.9~77  44.7~45 ViewMore> gotoslidegotoslidegotoslide Breakdowntoughconceptsthroughsimplevisuals. Mathwillnolongerbeatoughsubject,especiallywhenyouunderstandtheconceptsthroughvisualizations. BookaFreeTrialClass     TryThese!> gotoslidegotoslide   FAQsonSignificantFigures  Whatare SignificantFigures? SignificantFiguresrefertothenumberofimportantsingledigitsfrom0to9inthecoefficientoftheexpressionthatconveysthemessageaccurately.Thesesignificantfigureshelpengineersorscientistsinassertingthequantityofanymeasurement,length,volume,ormass. WhydoweNeed SignificantFigures? Significantfiguresarethemainaspectsofstatisticsandmathematicsthatdealwithaccuracyandprecision.Theyalsohelpinshowinghowprecisetheendvalueis.Significantfigurescanbeusedinday-to-daylifeaswellbyanyonetofindouttheaccuratefigure.  WhatisRoundingOffNumbers? Roundingnumbersmakeanumbersimplerbutkeepthenumberclosetoitsvalue.Therounded-offnumbermaybelessaccuratebutitisrelativelyclose. Peopleroundoutnumbersinmanysituationsthattheyfaceintheirday-to-daylife.  HowdoesAccuracyRelatetoSignificantFigures? Theclosenessbetweenthemeasurementandtheaccuratenumberiscalledaccuracy.Accuracyhelpsinprovidingconsistentresultswithnoerroralongwithaccuracyintheresult.Oneofthemainaspectsofsignificantfigures isthenumberbeingasaccuratetothevalueormeasurementitself.  WhendoZerosbeConsideredSignificant? Zerosthatarepresentbetweentwonon-zerodigitsinthenumberareconsideredsignificant.Thezerocanbepresenteitherontheleftandrightsideofthedecimalpoint.Forexample-230.056herezeroisconsideredassignificantandtherefore,thesignificantnumbersaresix.Allthetrailingzerosafterthedecimalpointaresignificantwhileallthetrailingzerosinawholenumberarenon-significant. WhencantheValue beRoundedoff togetSignificantFigures? Whenthefirstdigitoftherounded-offdigitcanberemovedorwhenitishigherthanthenumber5,thatiswhenthevaluecanhavesignificantfigures. ExploremathprogramExplorecodingprogramDownloadFREEStudyMaterialsRoundingWorksheetsExploremathprogramExplorecodingprogramMathworksheetsandvisualcurriculumGet1-yearFREEaccess