significant

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook14SignificantFigures

SignificantFigures

Aleverbalanceudtoweighatruckloadofstonemaybeaccuratetothenear-

est100kg,givingareadingof15200kg,surementshould

bewritteninsuchawaythatapersonlookingatitwillunderstandthatitrepre-

ntsthemassofthetrucktothenearest100kg,thatis,thatthemassissome-

wherebetween15100kgand15300kg.

eyou

nlookingatyour

datatableshouldbeabletoethatthemeasurementwasmadeonabalance

uldnotstatethemeasurement

fromthelaboratorybalanceas0.2060ginsteadof0.206gbecauthebalance

wasnotnsitiveenoughtomeasure0.0001g.

Toconveytheaccuracyofmeasurements,allpeopleworkinginscienceu

ficantfigureisadigitthatreprentsanactual

1,5,and2are

significantfiguresbecauthebalancewasabletomeasureten-thousands,thou-

sands,ckbalancewasnotnsitiveenoughto

ore,thetwozerosarenot

softhefoil

rethreedecimalplacesinthismeasure-

ore,thismeasurementhasthree

massbeenstatedas0.2060g,afourthsignificantfig-

urewouldhavebeenincorrectlyimplied.

RulesforDeterminingSignificantFigures

Allarenonzerodigits.

Themeasurement

hasthree

significantfigures.

Alldigitsthatarenotzerosaresignificant.

rminewhetherazerois

significant,uthefollowingrules:

325mLofethanol

222

Allarenonzerodigits.

Themeasurement

hasfour

significantfigures.

1.325gofzinc

2222

A.

B.

NameClassDate

ProblemSolving

SkillsWorksheet

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HoltChemFile:Problem-SolvingWorkbook15SignificantFigures

NameClassDate

ProblemSolvingcontinued

Themeasurement

hasthree

significantfigures.

0.0572m2offoil

222

Zerosappearinginfrontofnonzerodigitsarenotsignificant.

Nonzerodigits

Themeasurement

hasone

significantfigure.

0.0002gofRNA

2

Nonzerodigits

2.

Zerostotheright

ofanumberandafter

adecimalpoint

Themeasurement

hasfour

significantfigures.

Zerostotheright

ofanumberand

afteradecimalpoint

Themeasurement

hassix

significantfigures.

Zerosattheendofanumberandtotherightofadecimalare

etweennonzerodigitsandsignificant

arestatementofRule1.

Nonzerodigits

97.00kgoftungsten

22

11

Nonzerodigits

1200.00cm3oflead

22

1111

3.

Zerosattheendofanumberbuttotheleftofadecimalmayor

azerohasbeenmeasuredoristhe

firstestimateddigit,therhand,ifthezero

hasnotbeenmeasuredorestimatedbutisjustaplaceholder,itis

alplacedafterthezerosindicatesthatthey

aresignificant.

4.

Zerobetween

nonzerodigits

Zerobetween

nonzerodigits

Themeasurement

hasthree

significantfigures.

Themeasurement

hasfive

significantfigures.

Nonzerodigits

40.7Lofammonia

22

Nonzerodigits

32006mofwire

222

Zerosappearingbetweennonzerodigitsaresignificant.

111

1.

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HoltChemFile:Problem-SolvingWorkbook16SignificantFigures

NameClassDate

ProblemSolvingcontinued

Themeasurement

hastwo

significantfigures.

Themeasurement

hasfour

significantfigures.

Decimalpointisprent,

sothezerosaresignificant.

Therulesaresummarizedinthefollowingflowchart:

11

Nonzerodigits

3400gofsulfur

22

Nonzerodigits

ygen

22

GeneralPlanforDeterminingSignificantFigures

Thereisno

decimalpoint.

Lookfornonzerodigits—

allofthemaresignificant.

Totalnumberofsignificant

figures

Lookforadecimalpoint.

Lookforzerosbetween

nonzerodigits—theyare

significant.

Thereisa

decimalpoint.

Lookforzerosattheendof

thenumber—theyare

significant.

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook17SignificantFigures

NameClassDate

ProblemSolvingcontinued

SampleProblem1

Determinethenumberofsignificantfiguresinthefollowingmeasure-

ments:

a.30040g

b.0.663kg

c.20.05mL

e.0.0008m

Solution

ANALYZE

Whatisgivenintheproblem?fivemeasurements

Whatareyouaskedtofind?thenumberofsignificantfiguresineachmeas-

urement

PLAN

Whatstepsareneededtodeterminethenumberofsignificantfiguresineach

measurement?

Applythestepsintheflowcharttodeterminethenumberofsignificantfigures.

atethestepsthatarenot

applicabletothemeasurementinquestion.

ItemsData

abcde

0.0008g

quantity

Howmanynonzerodigitsarethere??

Howmanyzerosaretherebetweennonzerodigits??

Isthereadecimalpoint??

Howmanysignificantzerosareattheendofthenumber??

Totalnumberofsignificantfigures?

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook18SignificantFigures

NameClassDate

ProblemSolvingcontinued

SOLVE

a.30040g

Thefinalzeroisnotsignificant.

b.0.663kg

Thezeroonlylocatesthedecimalpointandisnotsignificant.

c.20.05L

Thereisadecimalfollowingthefinaltwozeros,soalldigitsaresignificant.

Howmanynonzerodigitsarethere?2

Howmanyzerosaretherebetweennonzerodigits?2

Isthereadecimalpoint?no

Howmanysignificantzerosareattheendofthenumber?NA

Totalnumberofsignificantfigures4

Howmanynonzerodigitsarethere?3

Howmanyzerosaretherebetweennonzerodigits?NA

Isthereadecimalpoint?yes

Howmanysignificantzerosareattheendofthenumber?NA

Totalnumberofsignificantfigures3

Howmanynonzerodigitsarethere?2

Howmanyzerosaretherebetweennonzerodigits?2

Isthereadecimalpoint?yes

Howmanysignificantzerosareattheendofthenumber?NA

Totalnumberofsignificantfigures4

Howmanynonzerodigitsarethere?2

Howmanyzerosaretherebetweennonzerodigits?NA

Isthereadecimalpoint?yes

Howmanysignificantzerosareattheendofthenumber?2

Totalnumberofsignificantfigures4

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook19SignificantFigures

NameClassDate

ProblemSolvingcontinued

e.0.0008g

enotsignificant.

EVALUATE

Aretheanswersreasonable?

Yes;allanswersareinagreementwiththerulesfordeterminingsignificant

figures.

Practice

inethenumberofsignificantfiguresinthefollowingmeasurements:

DETERMININGSIGNIFICANTFIGURESINCALCULATIONS

st

measurethevolumeinagraduatedcylinderthatisaccuratetothenearest0.1

ndeterminethemassofthesolutiononabalancethatcanmeasure

ereadeachmeasuringdeviceasaccurately

asyoucan,andyourecordthefollowingdata:

a.640cm3_____________________

b.200.0mL____________________

c.0.5200g_____________________

d.1.005kg_____________________

e.10000L_____________________

f.20.900cm___________________

g.0.00000056g/L______________

h.0.04002kg/m3_______________

i.790001cm2__________________

j.665.000kgؒm/s2______________

Howmanynonzerodigitsarethere?1

Howmanyzerosaretherebetweennonzerodigits?NA

Isthereadecimalpoint?yes

Howmanysignificantzerosareattheendofthenumber?NA

Totalnumberofsignificantfigures1

MeasurementData

Massofsolution,m11.079g

Volumeofsolution,V12.7mL

Densityofsolutioning/mL,D?

ans:2ans:5

ans:4ans:2

ans:4ans:4

ans:4ans:6

ans:1ans:6

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook20SignificantFigures

NameClassDate

ProblemSolvingcontinued

Youcandeterminedensityonyourcalculatorandgetthefollowingresult:

Dϭ

ᎏ

m

V

ᎏ

ϭ

ᎏ

1

1

1

2

.

.

0

7

7

m

9

L

g

ᎏ

ϭ0.872362204g/mL

Althoughthenumbersdivideouttogivetheresultshown,itisnotcorrecttosay

erthatyouaredealing

withmeasurements,erthefactthatyoumeasuredthe

massofthesolutionwithabalancethatgaveareadingwithfivesignificantfig-

ures:tion,youmeasuredthevolumeofthesolutionwithagradu-

atedcylinderthatwasreadableonlytothreesignificantfigures:s

oddtoclaimthatyounowknowthedensitywithanaccuracyofninesignificant

figures.

Youcancalculatethedensity—oranymeasurement—onlyasaccuratelyas

theleastaccurate

cathe

leastaccuratemeasurementwasthevolumebecauthemeasuringdeviceyou

udwascapableofgivingyouameasurementwithonlythreesignificantfigures.

Therefore,youcanstatethedensitytoonlythreesignificantfigures.

RulesforCalculatingwithMeasuredQuantities

Intheexamplegivenabove,youmustroundoffyourcalculatorreadingtoa

ca,youwouldsay:

Dϭϭ

m

V

ϭ0.872362204g/mLϭ0.872g/mL

11.079g

12.7mL

OperationRule

Multiplicationanddivision•Roundoffthecalculatedresulttothesamenumber

ofsignificantfiguresasthemeasurementhavingthe

fewestsignificantfigures.

Additionandsubtraction•Roundoffthecalculatedresulttothesamenumber

ofdecimalplacesasthemeasurementwiththe

eisnodecimalpoint,

roundtheresultbacktothedigitthatisinthesame

positionastheleftmostuncertaindigitinthequanti-

tiesbeingaddedorsubtracted.

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook21SignificantFigures

NameClassDate

ProblemSolvingcontinued

SampleProblem2

Inanexperimenttoidentifyanunknowngas,itisfoundthat1.82Lof

thedensityofthegasing/L?

Solution

ANALYZE

Whatisgivenintheproblem?themeasuredmassandvolumeofthegas

Whatareyouaskedtofind?thedensityofthegas

PLAN

Whatstepisneededtocalculatethedensityofthegas?

Dividethemassmeasurementbythevolumemeasurement.

Whatstepsarenecessarytoroundthecalculatedvaluetothecorrectnumberof

significantfigures?

he

calculatedresulttothatnumberofsignificantfigures.

COMPUTE

EVALUATE

Aretheunitscorrect?

Yes;densityisgiveninunitsofmassperunitvolume.

Arethesignificantfigurescorrect?

Yes;themasshadonlythreesignificantfigures,sotheanswerwasroundedto

threesignificantfigures.

ϭ2.98g/L2.983516484ϭϭ

D

gas

ϭ

m

gas

V

gas

foursignificantfigures

threesignificantfigures

5.430groundtothreesignificantfigures

1.82L

thedigitfollowingthe8is

lessthan5,sothe8remains

unchanged

D

gas

ϭ

roundtocorrect

significantfiguresϭ

m

gas

V

gas

numericalresultroundedresult

ItemsData

Massofthegas,m

gas

5.430g

Volumeofthegas,V

gas

1.82L

Densityofthegas,D

gas

(numericalresult)?g/L

Leastnumberofsignificantfiguresinmeasurements3(in1.82L)

Densityofthegas,D

gas

(rounded)?g/L

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook22SignificantFigures

NameClassDate

ProblemSolvingcontinued

Istheanswerreasonable?

Yes;themass/volumeratioisroughly3/1,sothedensityisapproximately3g/L.

Practice

mthefollowingcalculations,andexpresstheresultinthecorrectunits

andnumberofsignificantfigures.

a.47.0Ϭ2.2sans:21m/s

b.140cmϫ35cmans:4900cm2

c.5.88kgϬ200m3

ans:0.03kg/m3

d.0.0050m2ϫ0.042mans:0.00021m3

e.300.3LϬ:1.67L/s

f.33.00cm2ϫ2.70cmans:89.1cm3

g.35000kJϬ0.250minans:140000kJ/min

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook23SignificantFigures

NameClassDate

ProblemSolvingcontinued

SampleProblem3

Threestudentsmeasurevolumesofwaterwiththreedifferentdevices.

Theyreportthefollowingvolumes:

DeviceVolumemeasured

Largegraduatedcylinder164mL

Smallgraduatedcylinder39.7mL

Calibratedburet18.16mL

Ifthestudentspourallofthewaterintoasinglecontainer,whatisthe

totalvolumeofwaterinthecontainer?

Solution

ANALYZE

Whatisgivenintheproblem?threemeasuredvolumesofwater

Whatareyouaskedtofind?thetotalvolumeofwater

PLAN

Whatstepisneededtocalculatethetotalvolumeofthewater?

Addtheparatevolumes.

Whatstepsarenecessarytoroundthecalculatedvaluetothecorrectnumberof

significantfigures?

hecalcu-

latedresulttothatnumberofdecimalplaces.

COMPUTE

V

totalϭV1ϩV2ϩV3ϭ164mLϩ39.7mLϩ18.16mL

164mL

ϩ39.7mL

ϩ18.16mL

221.86mL

Roundthesumtothesamenumberofdecimalplacesasthemeasurementwith

thefewestdecimalplaces(164mL).

mLϭ222mL221.86

V

total

ϭ

thedigitfollowingthe1is

greaterthan5,sothe1is

roundedupto2

ItemsData

Firstvolumeofwater164mL

Secondvolumeofwater39.7mL

Thirdvolumeofwater18.16mL

Totalvolumeofwater?

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook24SignificantFigures

NameClassDate

ProblemSolvingcontinued

EVALUATE

Aretheunitscorrect?

Yes;thegivenvalueshaveunitsofmL.

Arethesignificantfigurescorrect?

Yes;threesignificantfiguresiscorrect.

Istheanswerreasonable?

Yes;estimatingthevaluesas160,40,and20givesasumof220,whichisvery

neartheanswer.

Practice

mthefollowingcalculationsandexpresstheresultsinthecorrectunits

andnumberofsignificantfigures:

a.22.0mϩ5.28mϩ15.5mans:42.8m

b.0.042kgϩ1.229kgϩ0.502kgans:1.773kg

c.170cm2ϩ3.5cm2Ϫ28cm2

ans:150cm2

d.0.003Lϩ0.0048Lϩ0.100Lans:0.108L

e.24.50dLϩ4.30dLϩ10.2dLans:39.0dL

f.3200mgϩ325mgϪ688mgans:2800mg

g.14000kgϩ8000kgϩ590kgans:23000kg

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook25SignificantFigures

NameClassDate

ProblemSolvingcontinued

AdditionalProblems

inethenumberofsignificantfiguresinthefollowingmeasurements:

a.0.0120m

b.100.5mL

c.101g

d.350cm2

e.0.97km

hefollowingquantitiestothespecifiednumberofsignificantfigures:

a.5487129mtothreesignificantfigures

b.0.013479265mLtosixsignificantfigures

c.31947.972cm2tofoursignificantfigures

d.192.6739m2tofivesignificantfigures

e.786.9164cmtotwosignificantfigures

f.389277600Jtosixsignificantfigures

g.225834.762cm3tovensignificantfigures

mthefollowingcalculations,andexpresstheanswerinthecorrect

unitsandnumberofsignificantfigures.

a.651cmϫ75cm

b.7.835kgϬ2.5L

c.14.75LϬ1.20s

mthefollowingcalculations,andexpresstheanswerinthecorrect

unitsandnumberofsignificantfigures.

a.7.945Jϩ82.3JϪ0.02J

b.0.0012mϪ0.00045mϪ0.00011m

c.500gϩ432gϩ2g

d.31.2kPaϩ0.0035kPaϪ0.147kPa

e.312dLϪ31.2dLϪ3.12dL

f.1701kgϩ50kgϩ43kg

sitsareawiththeproper

numberofsignificantfiguresinthespecifiedunit:

2

2

2

d.360cmϫ51cmϫ9.07cm

e.5.18mϫ0.77mϫ10.22m

f.34.95gϬ11.169cm3

f.1000kg

h.0.4936L

i.0.020700s

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook26SignificantFigures

NameClassDate

ProblemSolvingcontinued

tsvolumewiththe

propernumberofsignificantfiguresinthespecifiedunit:

3

3

3

thedensityofthe

liquidinthefollowingmeasurements?

/m3

b.g/mL

/dm3

mthefollowingcalculations,andexpresstheresultsinthecorrect

unitsandwiththepropernumberofsignificantfigures.

a.13.75mmϫ10.1mmϫ0.91mm

b.89.4cm2ϫ4.8cm

c.14.9m3Ϭ3.0m2

d.6.975mϫ30mϫ21.5m

thevolumeofaregionofspacethatmeasures752mϫ319mϫ110m?

Giveyouranswerinthecorrectunitandwiththepropernumberofsignifi-

cantfigures.

mthefollowingcalculations,andexpresstheresultsinthecorrect

unitsandwiththepropernumberofsignificantfigures.

a.7.382gϩ1.21gϩ4.7923g

b.51.3mgϩ83mgϪ34.2mg

c.0.007LϪ0.0037Lϩ0.012L

d.253.05cm2ϩ33.9cm2ϩ28cm2

e.14.77kgϩ0.086kgϪ0.391kg

f.319mLϩ13.75mLϩ

inermeasures30.5mmϫ202mmϫisfullofa

liquid,impty,ithasamassof0.30kg.

Whatisthedensityoftheliquidinkilogramsperliter?

7.76kmofwirehasamassof3.3kg,whatisthemassofthewireing/m?

Whatlengthinmeterswouldhaveamassof1.0g?

inerofplantfoodrecommendsanapplicationrateof52kg/

containerholds10kgofplantfood,howmanysquaremeterswillitcover

(1haϭ10000m2)?

therateinkilojoulesperminute?Whatistherateinkilojoulespercond?

Copyright©byHolt,htsrerved.

HoltChemFile:Problem-SolvingWorkbook27SignificantFigures

NameClassDate

ProblemSolvingcontinued

pipefillsacontainerthatmeasures189cmϫ307cmϫ272cmin97s.

thevolumeofthecontainerincubicmeters?

therateofflowinthepipeinlitersperminute?

therateofflowincubicmetersperhour?

mthefollowingcalculations,andexpresstheresultsinthecorrect

,inproblems

withmultiplesteps,itisbettertoperformtheentirecalculationandthen

roundtosignificantfigures.

a.(0.054kgϩ1.33kg)ϫ5.4m2

b.67.35cm2Ϭ(1.401cmϪ0.399cm)

c.4.198kgϫ(1019m2Ϫ40m2)Ϭ(54.2sϫ31.3s)

d.3.14159mϫ(4.17mϩ2.150m)

e.690000mϬ(5.022hϪ4.31h)

f.(6.23cmϩ3.111cmϪ0.05cm)ϫ14.99cm