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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 ________________________________________________________________________