Rounding off Significant Figures

To round it off to 3 significant figures, we require to round it off to 6 decimal places after the decimal point. 0.0001366 = 0.000137 correct to 3 significant ... SignificantFigures Inroundingoffsignificantfiguresorsignificantdigitswewillbeveryusefulbecauseitenablesustosimplifycomplexcalculation. Wewillabout……..   ●Rulestofindthenumberofsignificantfigures   ●Roundingoffadecimaltotherequirednumberofsignificantfigures   ●Roundofftoaspecialunit. WhatareSignificantfigures?Ifwehavetofindthespeedofcarwiththehelpofspeedometer,weobservethatthespeedliesbetween92.4km/hrand92.5km/hr.Bycloseobservation,wecansayapproximatelythatthespeedofcaris92.46km/hr.Thelastdigit6ishoweveruncertain.  Thus,significantfiguresareallcertaindigitsinameasurementplusoneuncertaindigit.Theuseofsignificantfiguresinmeasurementandvalueisaformofrounding. Thus,intheaboveexample,wesaythat92.46km/hrhasfoursignificantfigures. Rulesforfindingthenumberofsignificantfigures: 1.Allnon–zeronumbers(1,2,3,4,5)arealwayssignificant. Forexample;  ●1325hasfoursignificantfigures  ●235.14hasfoursignificantfigures 2.Allzerosbetweennon-zeronumbersarealwayssignificant. Forexample;  ●204.003hassixsignificantfigures.  ●50.00hasfoursignificantfigures.  ●51.02010hassevensignificantfigures. 3.Inadecimalnumberwhichliesbetween0and1,allzeroswhicharetotherightofthedecimalpointbuttotheleftofnon-zeronumberarenotsignificant. Forexample;  ●0.00247hasonlythreesignificantfigures.  ●0.002030hasfoursignificantfigures. 4.Inawholenumberiftherearezerostotheleftofanunderstooddecimalpointbuttorightofanon-zerodigitthecasebecomesdoubtful. Inthenumber402000,thereisaunderstooddecimalpointafterthegivensixdigits.Thereare3zerosthatlietotheleftoftheunderstooddecimalpointbuttotherightofanon-zeronumbersothecasebecomesdoubtful. Ifitisexpressedas4.02×10⁵,itbecomesclearandwecansaythat4.02×10⁵has3significantfigures.Itisexpressedas4.020×10⁵,thenthenumberofsignificantfiguresis4. 5.Whenadecimalisroundofftoagivennumberofdecimalplaces,allthefinalzerosinadecimalnumberaresignificant. Forexample; Ifweroundoff6.785totwodecimalplaces,weget6.80whichhas3significantfigures. Roundingoffdecimalstotherequirednumberofsignificantfigures: Roundingoffthenumbercorrecttothreesignificantfigures (1)53.214→Ithas5significantfigures. Toroundoffitto3significantdigits,werequiredtorounditoffto1placeafterthedecimal. Therefore,53.214=53.2roundedoffto3significantfigures. [Thedigitinhundredthsplaceis1whichislessthan5.So,thedigitinthetenthsplaceremains2andthedigits1and4disappear.] (2)4.3062→Ithas5significantfigures.Torounditoffto3significantfigureswerounditofftothe2ⁿᵈplaceafterthedecimalpoint. So,4.3062=4.31correcttothreesignificantfigures. (3)30.002→Ithas5significantfigures.Torounditoffto3significantfigures,werequiredtorounditoffto1decimalplaceafterthedecimalpoint. 30.002=30.0correctto3significantfigures. (4)0.0001378→Ithas4significantfigures.Torounditoffto3significantfigures,werequiretorounditoffto6decimalplacesafterthedecimalpoint0.0001378=0.000138correctto3significantfigures. (5)0.0001366→Ithas4significantfigures.Torounditoffto3significantfigures,werequiretorounditoffto6decimalplacesafterthedecimalpoint. 0.0001366=0.000137correctto3significantfigures. (6)7.304→7.30correctto3significantfigures. (7)4.888→4.89correctto3significantfigures. (8)5.999→6correctto3significantfigures. Examplestoroundoffthefollowingmeasurements: (i)1273.866kgcorrectto6significantfigures.Ithas7significantfigures.Torounditoffto6significantfigures,werounditoffto2decimalplaceafterthedecimalpoint. Therefore,1273.866=1273.87correctto6significantfigures. (ii)203.102gcorrectto4significantfigures.Ithas6significantfigures.Torounditoffto4significantfigures,werounditoffto1ˢᵗdecimalplaceafterthedecimalpoint203.102=203.1correctto4significantfigures. (iii)1.0718mgcorrectto2significantfigures.Ithas5significantfigures.Torounditoffto2significantfigures,werounditoffto1ˢᵗdecimalplaceafterthedecimalpoint. 1.0718=1.1correctto2significantfigures. (iv)0.003674kmcorrectto1significantfigure.Ithas4significantfigures.Torounditoffto1significantfigure,werounditoffto3placesafterthedecimalpoint. Therefore,0.003674=0.004correctto1significantfigure. Examplestoroundingofftoaspecifiedunit (i)Roundoff$65437tothenearest10dollars. $65440tothenearestdollar (ii)Roundoff$198.287tothenearest10cents. Toroundoff198.287tothenearest10cents,wehavetorounditoffto1placeofdecimal. =$198.30 (iii)Roundoff782.58tothenearestdollar. Toroundoff782.58tothenearestdollar,wehavetorounditofftothenearestwholenumber. Therefore,$782.58=$783roundedtothenearestrupeedollar. (iv)Roundoff475.095tothenearestcents. Toroundoff475.095tothenearestcents,wehavetorounditoffto2placesofdecimal.475.095roundedofftothenearestcentsis475.10. (v)Roundoff18.066cmtothenearestmm. Since,1mm=0.1cm,sotorounditofftothenearestmm,wehavetorounditofftoonedecimalplaces. 18.066cm=18.1cmroundedofftothenearestmmor181mm. (vi)Roundoff53.4278mtothenearestcm. Since,1cm=0.01m,weroundoff53.4278mtothenearestcm.Wehavetorounditofftotwoplacesofdecimal. 53.427m=53.43mroundedofftothenearestcmor5343cm. (vii)0.00737kgtonearestg. Since,1g=0.001kgsotoroundoff0.00737kgtothenearestg,wehavetorounditofftothreeplacesofdecimal. Therefore,0.00737kg=0.007kgroundedofftothenearestg. (viii)17.2262gtothenearestmg. Since,1mg=0.001gsotoroundoff17.2262gtothenearestmg,wehavetorounditofftothreeplacesofdecimal. Therefore,17.2262g=17.226groundedofftothenearestmg. ● SignificantFiguresSignificantFigures● SignificantFigures-WorksheetsWorksheetonSignificantFigures 8thGradeMathPractice FromSignificantFigurestoHOMEPAGE New!CommentsHaveyoursayaboutwhatyoujustread!Leavemeacommentintheboxbelow.AskaQuestionorAnsweraQuestion. Didn'tfindwhatyouwerelookingfor?Orwanttoknowmoreinformation aboutMathOnlyMath. UsethisGoogleSearchtofindwhatyouneed. Sharethispage: What’sthis? 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