Unit 1: Measurement Lab · PDF file3 Unit 1: Measurement & Lab Equipment Abstract This lab...

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Unit1:Measurement&LabEquipment AbstractThislabreviewstheconceptofscientificmeasurement,whichyouwillemployweeklythroughoutthiscourse. Specifically,wewillreviewthemetricsystemsothatyouwillbeabletomeasurelength,mass,volumeandtemperatureinmetricunits,andconvertbetweentheEnglishandmetricsystems. Youwillalsofamiliarizeyourselfwithcommonlaboratoryequipment. Youwillreviewandpracticescientificnotationsothatyouwillunderstanditsuseinscientificmeasurement. Finally,youwillutilizebasicstatisticalmethodstoevaluatedatathatyougatherandgraph. Thesectionsentitled“PutwhatyouhavereadintoPractice”willbedueashomeworknextweek.Whateveryoudonotcompleteduringthelabperiodshouldbecompletedathome.

1.1 Conversionswithin theMetricSystem Introduction Length,Mass,VolumeToconvertwithinthemetricsystem,youmustrememberthefollowing:

meters,

k h da liters, d c m µ n ρ Kilo‐‐‐‐‐‐‐‐‐hecto‐‐‐‐‐‐‐‐‐Deka‐‐‐‐‐‐‐‐‐‐‐‐grams ‐‐‐‐‐‐‐‐‐deci‐‐‐‐‐‐‐‐‐centi‐‐‐‐‐‐‐‐‐milli‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐micro‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐nano‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐pico103 102 101 100 10‐‐‐1 10‐‐‐2 10‐‐‐3 10‐‐‐6 10‐‐‐9 10‐‐‐12        Toconvertbetweenmetricunits,youwillneedtomovethedecimaltotherightortotheleft,relativetowhereyoubegin,asshownbythischart. Thismeansthatyouwillneedtoaddadecimaltotheendofanywholenumber! Forinstance“35”isthesameas“35.” 

Example1: Convert5mgtog. Togetfrommgtogrequiresyoutomovetotheleftonthechart3units,therebymovingthedecimaltotheleft3units.Thereforethevaluewillbe0.005g.

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Example2: Convert80hectoliterstocentiliters. Togetfromhectotocentirequiresyoutomovetotheright4units. Thereforethenumberwillbecome800000cl. 

Example3: Convert400mltonl. Togetfrommillitonanorequiresyoutomove6unitstotheright. Noticethatwearereferringtotheexponentassociated

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with10whenwecountplacestomovethedecimal‐‐‐wearenotcountingactualwordslistedonthechart. Therefore400mlbecomes400,000,000nl.*Makesureyoulookatyouranswertoseeifitmakessense! Doesitmakesensethat1literisthesameas0.001ml?! No,becausemillilitersaresmallerunitsthanliters! Thereforeyouwouldknowthatyouhadmovedthedecimalthewrongway.Oneliterisequalto1000ml. Importantconversionstoknowaboutwaterunderstandardconditions!

1cc=1ml 1dm3=1liter1ml=1g 1liter=1kg

 Thismeansthat50mlofwaterweighs50g.Also,3litersofwaterequals3kg. Checkyourunderstanding: Ifyouweigh142mlwater,howmanymgwoulditequal?

TemperatureTemperaturecanbemeasuredinFahrenheitorinCelsius. HereintheUSweareusedtothinkingoftemperatureintermsof°F. InscienceweevaluatetemperatureusingtheCelsiusscale. Itiscalledthecentigradethermometerbecausethereare100(centi)degreesbetweenthefreezing(0°C)andboilingpoint(100°C)ofwater.Toconvertbetweenthetwo,usethefollowingconversions: FromFahrenheittoCelsius:1. Subtract32fromdegreesFahrenheit2. Multiplyby53. Divideby9 FromCelsiustoFahrenheit:1. MultiplydegreesCelsiusby92. Divideby53. Add32 TogetyouthinkingintermsofCelsius,knowthefollowingcommonknowledgepoints. Thiswillhelpyouevaluateyouranswerintermsof“doesthismakesense”?

Freezing:0°C=32°FRoomTemperature: 21.1°C=70°FBodyTemperature: 37°C=98.6°FBoiling: 100°C=212°F

 Example1:Whatisthetemperaturein°Ciftheoutsideairtemperatureis43°F?

1.43‐‐‐32=112.11x5=553.55dividedby9=6.11

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Thereforetheansweris6.11°C. Evaluatetheanswer. Doesthismakesense? Yes,inthatyouwouldexpectthetemperatureinCelsiustobelessthananequaltemperatureinFahrenheit,basedontheabove“commonknowledge”points.

Putwhatyouhavereadintopractice:Convertthefollowingnumberstotheunitsindicated. Indicatewhateacharemeasuring‐‐‐aretheyunitsofmass,volume,orlength? 

1. 5.5mg= hg Unitof:  

2. 61pl= ml Unitof:  

3. 110m= km Unitof:  

4. 7.89dg= µg Unitof:  

5. 0.003km= mm Unitof:  

Convertthefollowingtemperaturesasindicted. Youmustshowyourwork. Donotuseacalculator! 

6.83◦F= ◦C 9. 98◦C= ◦F    

 7.22◦C= ◦F 10. 62◦F= ◦C

 8. 4◦C= ◦F

1.2 ConvertingfromEnglishtoMetricUnits  

ConvertingfromEnglishtometricunits: 

Thebasicmetricunitoflengthisthemeter. TocompareEnglishandmetricvaluesoflength,itishandytoknowthat1inch=2.54cm. Massisexpressedingrams. TocompareEnglishandmetricvaluesofmass,itishandytoknowthat1kilogram=2.21pounds.

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Volumeismeasuredinliters. TocompareEnglishandmetricvaluesofvolume,itishandytoknowthat1ounce=30millilitersand1gallon=3.8liters.

1.3 Becoming familiarwithLaboratoryEquipment Inthislabcourse,youwillworkwithequipmentandglasswarethatiscommoninthelaboratorysetting. Locatethefollowingitems.

Graduatedcylinder DigitalBalance StirBarBeaker Graduated Pipette  

Erlenmeyerflask Weigh boat  

TripleBeamBalance Hot/Stir Plate   

***Usethespacebelowtomakeasketchofeachofthemsothatyouwillrecognizeitinthefuture.

MeasuringVolume:Fillyourgraduatedcylinderwith45mlofwater. Whenmeasuringthevolumeofaliquidinagraduatedcylinder,youwillobservea“meniscus.”Locatethemeniscus(andincludeitinyourdrawing.) Doyouthinkthatyoushouldmeasurethevolumefromthetoporbottomofthemeniscus? Checkwithyourinstructortomakesureyouarecorrect!

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 Nowtransferthewatertoyourbeaker. Isthisasaccurateatmeasuringvolumeasthegraduatedcylinder?

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UsingaBalance:Forthedigitalandtriplebeambalance,practiceusingeachbyfindingthemassofacoin. Todothis,youwillneedtouseaweighboatsinceyoutypicallydonotwanttoplacethematerialyouareweighingdirectlyonthebalance. 

1. Locateandplacetheweighboatonthedigitalbalance,onthetriplebeambalance,youmaysetthecoinonthemetalpanwithouttheweighboat. 

2. “Tare”thedigitalbalanceinordertoresetthebalanceto“0”grams. Thiswillensurethatyoudonotaddtheweightoftheweighboattowhatyouareweighing. Makesurethatyourtriplebeambalancesettozeroaswellbyusingtheadjustmentknobunderneaththepan. 

3. Addthecoin. Recordtheweightofthecoinforeach.Triplebeam gramsDigitalbalance grams

 4. Whichbalanceismoreaccurate,andwhy?

Putwhatyouhavereadintopractice:Nowyouwillapplytheknowledgeyouhavegained. Inthissectionofthelab,youwilllearnaboutthedifferentpiecesoflaboratoryequipment,aswellashowtomeasurethedifferentpropertiesofmatterwiththem. UsingaBalance:

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 DigitalBalance:Havingimproperweightsmayprovideoddresultsonyourexperiments.Inmostexperimentsquantitiesmaybecrucialtoexpectaccurateresults.Thedigitalbalancewillprovideyouwiththeexactweightofthematerialsyouwillneednotonlyonthebiologylaboratorybutinanyotherlabs;thisiswhyusingitcarefullyisvitalforyourexperiments.1. Turnonthedigitalweight.2. Placeaweightboatonthescale.3. ResetthevaluesofthescalebypressingON/ZERObuttonlocatedontheleftof

thescale.4. Pourthesubstanceyouwillbeneedingtoweightintotheweightboat.5. Ifyoupourextraquantitiesmakesureyougetridoftheexcessbygrabbingan

spatulaanddisposingoftheexcess.Duringapractical,SallyStudentandSidStudentwereaskedtofindtheweightofapennyonadigitalbalance. Sallyfoundthattheweightwas0.001gramswhereasSidfoundthattheweightwas4.3grams. Thecorrectanswerwas2.5grams. a. WhatdoyouthinkSallymighthavedoneincorrectly?

    b. WhatmightSidhavedoneincorrectly?

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UnderstandingMeters: 1. Metersarethebaseunitofthemetricsystemusedtomeasurelength. Pleasestatewhatmeasuringdeviceordevicesyouwouldusetomeasureanobjectinthefollowingunits: 3mm:

20cm:

1.5m:   

2. Findtwoitems:onemeasuredincentimeters(cm)and,ifpossible,onemeasuredinmillimeters(mm). Usetheinstrumentsthatyoulistedin#1tomeasuretheseobjects. Writedownthenameoftheitemandhowmanycentimetersormillimetersitmeasures. Pleaseincludetheunits(cmormm)withyourmeasurement.

    3. Isacentimeterlargerorsmallerthanamillimeter?

    4. Whatpropertyoftheseitemsdocmormmmeasure: length,volume,massortemperature?

    5. Theheightoftheaveragepersonisalittleover1.5meters. Knowingthis,isonecentimeterlargerorsmallerthanonemeter?

6. Isonemillimeterlargerorsmallerthanonemeter? 

7. Runnersoftenruna5K,whichisfivekilometers(km). Isakilometerlargerorsmallerthanameter?

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Understandinggrams: 8. Gramsarethebaseunitofthemetricsystemusedtomeasuretheamountofmatterinanobject. Therearetwoinstrumentsthatyoucouldusetomeasuresomethingingrams. Pleaselistthosetwoinstrumentshere(note: youwilldrawtheseinstrumentslater).

9. Findoneitemthatismeasuredingrams(g).Writedownthenameoftheitemandhowmanygramsitweighs. Pleaseincludetheunits(g)withyourmeasurement.

10. Findoneitemthatismostlikelymeasuredinkilograms(kg). Areyouabletomeasurethiswiththeinstrumentsthatyoulistedinquestion8? Whyorwhynot?

    11. Whichitemfeltheavier,theitemmeasuredingramsortheitemmeasuredinkilograms?

12. Basedoffofyouranswertonumber8,isagramlargerorsmallerthanakilogram?

13. Whatcharacteristicoftheseitemsdogramsandkilogramsmeasure: length,volume,mass,ortemperature?

    14. Theotherunitsthatcanbeusedtomeasuretheseitemsareeitherpoundsorounces. Thesearecommonlyusedtomeasuretheweightofobjects. Whatpropertyoftheitem(s)doesweightmeasure? Isthispropertythesamethingasyouranswerinnumber13?

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UnderstandingLiters: 15. Litersarethebaseunitofthemetricsystemusedtomeasurevolume. Pleaselistallofthepiecesofglasswarethatcouldbeusedtomeasurevolume.

16. Ifyouweretopicktwoofthesepiecesofglasswaretomeasurethevolumeofaliquidasaccuratelyaspossible,whichtwowouldyoupick? Why?

17. Findoneitemthatisusedtomeasureliters(l). Findoneitemthatisusedtomeasuremilliliters(ml). Writedownthenameoftheitemandhowmanylitersormillilitersitmeasures. Pleaseincludetheunits(lorml)withyourmeasurement.

    18. Whichitemwaslarger,theoneusedtomeasurelitersortheoneusedtomeasuremilliliters?

19. Basedoffofyouranswerinnumber17,wouldyoubeabletoplaceallofthecontentsofa2litercontainerintoa1000mlcontainer?

20. Wouldyoubeabletoplacethecontentsofa1litercontainerintoa600mililitercontainer?

 21. Whatcharacteristicofthecontentsofthecontainerdolitersmeasure: length,volume,gramsortemperature?

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1.4 Scientific NotationIntroduction: ScientificNotationisawayofexpressionverylargeorverysmallnumberssuchthatitiseasytowrite,easytodeterminethevalueandeasytomakecomparisonstoothernumbers.Forinstance:

• thenumber342000033994isalongnumbertowriteanddifficulttosayexactlywhatthatnumber’svalueiswithoutsomethought. Addingcommashelps:342,000,033,994,whileeasiertoreadisstilllargeandlong!

 • howdoes342000033994compareto45645612825? Howabout

342,000,033,994to45,645,612,825‐‐‐howmuchbiggerorsmallerisit? Thisisveryhardtodoataglance!

 Puttingthenumbersinscientificnotationmakesiteasytoquicklydeterminethevalueandtocomparenumbers.

Try3.42x1011vs.4.56x1010? Itismucheasiertocomparethesevalues! ScientificNotationisNOTdifficult,butdoesrequirethatyoufollowsomesimplesteps,andthatyouuseyourcommonsense. Followthesestepseachtime: 

1. Rewriteyournumberandputadecimalpointafterthe*first*nonzerodigit. Forinstance,

a.1234567becomes1.234567andb.0.001234567becomes1.234567

2. Add“x10”totheendofthedigitsa.1234567becomes1.234567x10andb.0.001234567becomes1.234567x10

3. Counthowmanyplacevaluesthedecimalhasmovedfromtheoriginalplacementtothecurrentplacement. Writethatnumberasyourexponent.

a. Ifthenumberbecamesmallerwhenyoumovedthedecimal,youwillneedtheexponenttobepositive:1234567becomes1.234567x106

b. Ifthenumberbecamebiggerwhenyoumovedthedecimal,youwillneedtheexponenttobenegative:0.001234567becomes1.234567x10‐‐‐3

4. Alwayscheckyouranswers! Dotheymakesense? Forinstance:Does1.234567x106equalalargernumberby6tens,1234567? Yes!

 Whatdotheexponentsmean,ataglance? Rememberthesevaluesandyouwillbeabletoreadthevalueofverylargenumbersveryquickly. 103:thousands 106:millions 109:billions

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10‐‐‐3:thousandths 10‐‐‐6:millionths 10‐‐‐9: billionths Putwhatyouhavereadintopractice:Convertthefollowingnumbersfromfullexpressiontoscientificnotation.

1. 1,345,635,000  

2. 

457.430  

3. 

0.000554433  

4. 

47777.0055  

5. 

0.0044551111  

Convertthefollowingnumbersfromscientificnotationtofullexpression. 

6.4.56x108

7.6.785544x10‐‐‐8

8.8.992233x106

9. 9.11x10‐‐‐2

10.6.789x105  

1.5 StatisticalCalculations  

IntroductionToanalyzedatageneratedinthelaboratoryinordertodetermineitssignificance,youmustfirstbeequippedtoevaluateyourdatafromastatisticalperspective. Areviewofbasicstatisticaltermsisincludedhereforyourreview. 

Mean:Thisisanaverageofagroupofmeasurements.Howtocalculatemean?

Addallvaluesanddividebytotalnumberofvalues.• Example:values‐‐‐40,38,22,20,30Mean=40+38+22+40+30dividedby5=30

 Median:Thevaluethatisinthemiddleofagroupofmeasurements.Howtocalculatemedian?

Usingpreviousexample:• Example:values‐‐‐40,38,22,20,30

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Rearrangefromlowtohigh‐‐‐20,22,30,38,40Median=middle value = 30

 Range:Thedifferencebetweenthesmallestandthelargestmeasurements.Howtocalculaterange?

Usingpreviousexample:• Example:values‐‐‐40,38,22,20,30

Subtractsmallestvalue,20,fromlargestvalue,40Range=40–20=20

 Deviation:Measureshowthemeasurementsvaryfromthemean(+or‐‐‐).Inotherwords,whatisthedifferencebetweenanactualmeasurementandthemean,oraverage,ofthesample?Howtocalculateadeviation?

Usingpreviousexample:• Example:values‐‐‐40,38,22,20,30

Wedeterminedthemeantobe30. Thedeviationforthevalue“38”wouldbe+8. Thisvalueis8morethanthemean.

 Variance:Thismeasureshowmuchdifference,orvariation,thereisbetweenthevaluesyouhaveobtained. Thesmallerthevariance,thecloserthevalueswillbetothemean. Likewise,thelargerthevariance,thefartherthevalueswillbefromthemean.HowdoIcalculatevariance?

Calculatethesumofthesquareddeviationsdividedbythenumberofvaluesminusone. Usingpreviousexample:

• Example:values‐‐‐40,38,22,20,30(100+64+64+100+0)=82

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StandardDeviation:Standarddeviationgivesyouanideaofthewidelyspreadyourvaluesareaboutthemean. Thesmallerthestandarddeviation,thecloseryourvalueswillbetotheaverage. Ifyouweretographdatahavingasmallstandarddeviation,youwouldexpectatall,thinbellshapedcurve. Ontheotherhand,ifthestandarddeviationwerelarge,yourbellshapedcurvewouldbewider.HowtocalculateStandardDeviation?

Calculatethesquarerootofthevariance.Usingpreviousexample:

• Example:values‐‐‐40,38,22,20,30Thevarianceequaled82,todetermineStandardDeviationtakethesquarerootof82=9.06

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Note: Standarddeviationcanbeusedtoevaluatethepercentageofapopulationthatisnear“average”. Onestandarddeviationtotheleftandrightofthemeanwillcover68%ofthepopulation;twostandarddeviationstotheleftandrightofthemeanwillcover95%ofthepopulation.

Putwhatyouhavereadintopractice:Purpose: Inthisexerciseyouwillrecordthegenderandheightofeveryoneinthelab. Youwilldeterminetheaverageheightofmalesandfemalesinyourlabsection.

 MaterialsandMethods:MeterStickLabparticipants

 Haveeachindividuallisttheirgenderandheightonthewhiteboard. Recordthisinformationinthedatatableprovided. Wherenecessary,convertmeasurementsrecordedinEnglishunitstometriccentimeters. Usethespaceprovidedtorecorddeviations(requiredonnextpage).

 Results:Males(inches): Males(cm): Females (inches): Females(cm):

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Figure1:HeightmeasurementsofBiology1406laboratorypopulation

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Usethedatafromyourtabletocalculatethefollowing,usingtheinformationandexamplesofeachgivenpreviously(showyourwork!).Makesurethatyouusethedataexpressedincm,notinches!

________________________________________________________________________Sizeofsample:

 Males Females EntireClass ________________________________________________________________________Meanheight:

Males Females EntireClass ________________________________________________________________________ MedianHeight:

Males Females EntireClass ________________________________________________________________________Rangeofheight:

Males Females EntireClass ________________________________________________________________________