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Schaum's Outlines - Mathematics for Nurses, 2nd Edition.pdf

Schaum's Outlines - Mathematics…

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简介:本文档为《Schaum's Outlines - Mathematics for Nurses, 2nd Editionpdf》,可适用于人文社科领域,主题内容包含SCHAUM’SOUTLINEOFTheoryandProblemsofMATHEMATICSFORNURSESThispageintentiona符等。

SCHAUM’SOUTLINEOFTheoryandProblemsofMATHEMATICSFORNURSESThispageintentionallyleftblankSCHAUM’SOUTLINEOFTheoryandProblemsofMATHEMATICSFORNURSESSecondEditionEIZONISHIURA,PhDAssociateProfessorofMathematicsQueensboroughCommunityCollegeLARRYJSTEPHENS,PhDProfessorofMathematicsUniversityofNebraskaatOmahaLANACSTEPHENS,MSN,ARNPNursePractitioner,AlegentHealthOmaha,NebraskaSchaum’sOutlineSeriesMcGRAWHILLNewYorkChicagoSanFranciscoLisbonLondonMadridMexicoCityMilanNewDelhiSanJuanSeoulSingaporeSydneyTorontoCopyright,byTheMcGrawHillCompanies,IncAllrightsreservedManufacturedintheUnitedStatesofAmericaExceptaspermittedundertheUnitedStatesCopyrightActof,nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredinadatabaseorretrievalsystem,withoutthepriorwrittenpermissionofthepublisherXThematerialinthiseBookalsoappearsintheprintversionofthistitle:AlltrademarksaretrademarksoftheirrespectiveownersRatherthanputatrademarksymbolaftereveryoccurrenceofatrademarkedname,weusenamesinaneditorialfashiononly,andtothebenefitofthetrademarkowner,withnointentionofinfringementofthetrademarkWheresuchdesignationsappearinthisbook,theyhavebeenprintedwithinitialcapsMcGrawHilleBooksareavailableatspecialquantitydiscountstouseaspremiumsandsalespromotions,orforuseincorporatetrainingprogramsFormoreinformation,pleasecontactGeorgeHoare,SpecialSales,atgeorgehoaremcgrawhillcomor()TERMSOFUSEThisisacopyrightedworkandTheMcGrawHillCompanies,Inc(“McGrawHill”)anditslicensorsreserveallrightsinandtotheworkUseofthisworkissubjecttothesetermsExceptaspermittedundertheCopyrightActofandtherighttostoreandretrieveonecopyofthework,youmaynotdecompile,disassemble,reverseengineer,reproduce,modify,createderivativeworksbasedupon,transmit,distribute,disseminate,sell,publishorsublicensetheworkoranypartofitwithoutMcGrawHill’spriorconsentYoumayusetheworkforyourownnoncommercialandpersonaluseanyotheruseoftheworkisstrictlyprohibitedYourrighttousetheworkmaybeterminatedifyoufailtocomplywiththesetermsTHEWORKISPROVIDED“ASIS”McGRAWHILLANDITSLICENSORSMAKENOGUARANTEESORWARRANTIESASTOTHEACCURACY,ADEQUACYORCOMPLETENESSOFORRESULTSTOBEOBTAINEDFROMUSINGTHEWORK,INCLUDINGANYINFORMATIONTHATCANBEACCESSEDTHROUGHTHEWORKVIAHYPERLINKOROTHERWISE,ANDEXPRESSLYDISCLAIMANYWARRANTY,EXPRESSORIMPLIED,INCLUDINGBUTNOTLIMITEDTOIMPLIEDWARRANTIESOFMERCHANTABILITYORFITNESSFORAPARTICULARPURPOSEMcGrawHillanditslicensorsdonotwarrantorguaranteethatthefunctionscontainedintheworkwillmeetyourrequirementsorthatitsoperationwillbeuninterruptedorerrorfreeNeitherMcGrawHillnoritslicensorsshallbeliabletoyouoranyoneelseforanyinaccuracy,errororomission,regardlessofcause,intheworkorforanydamagesresultingtherefromMcGrawHillhasnoresponsibilityforthecontentofanyinformationaccessedthroughtheworkUndernocircumstancesshallMcGrawHillandoritslicensorsbeliableforanyindirect,incidental,special,punitive,consequentialorsimilardamagesthatresultfromtheuseoforinabilitytousethework,evenifanyofthemhasbeenadvisedofthepossibilityofsuchdamagesThislimitationofliabilityshallapplytoanyclaimorcausewhatsoeverwhethersuchclaimorcausearisesincontract,tortorotherwiseDOI:Xebookcopyrightxqxd:AMPageWanttolearnmoreWehopeyouenjoythisMcGrawHilleBook!Ifyoudlikemoreinformationaboutthisbook,itsauthor,orrelatedbooksandwebsites,pleaseclickhere,PREFACETOTHESECONDEDITIONMuchhaschangedinthefieldofnursingsince,whenthisbookwasfirstpublishedTheapothecarysystemhaspracticallydisappearedandhasbeenreplacedbythemetricsystemofmeasurementintheareaofmedicinedosagesClarkandFried’srulehavedisappearedasameansofestimatingasafedosageforachildbasedonhisorherweightandageMitchellJStoklosaandHowardAnsel,inthetentheditionofPharmaceuticalCalculations,statethat‘‘Todaytheserulesarenot,ingeneral,usedbecauseagealoneisnolongerconsideredasingularlyvalidcriterioninthedeterminationofchildren’sdosage,especiallywhencalculatedfromtheusualadultdose,whichitselfprovideswideclinicalvariationsinresponse’’Becauseofthis,wehavedroppedthesectionthatincludesClarkandFried’sruleWehavealsoreplacedallproblemsthatinvolveapothecarymeasurementsofdrugsForhistoricalreasons,wehaveleftthepartinChapterthatrelatesapothecarymeasurementstoothermeasurementsAlso,ifdrugshavedisappearedfromusewehaveleftthemoutofthebookIfadrugwasmentionedinexamplesorproblemsbutwecouldnotfindthatdrugintheNursingDrugHandbookorinthePhysicians,DeskReference,wereplaceditwithanotherdrugthatisinwideuseWehavecontinuedtheemphasisondimensionalanalysisintheworkingofproblemsandexamplesWehavereplacedsomeproblemstatementsbythelabelsthataccompanythedrugandaskforthecomputationgiventhatthedrugisavailableinthestrengthstatedonthelabelWehaveaddedachapteronstatisticsthatisintendedtohelpthenursewiththestatisticscoursethatsheorheisrequiredtotakeWehaveincorporatedintothischapteroutputfromMicrosoftExcelandMinitabthatnursesmayfindintegratedintotheircourseIhavetaughtacoursethatallnurseswhoenterthegraduatenursingprogramattheUniversityofNebraskaarerequiredtotakeInthiscourse,IintegrateExcelandMinitabIhavefoundnearlyallmystudentshaveExcelontheirownhomecomputersandaredelightedtobeintroducedtoitintheirstatisticscourseThenursingstudentwillbehappytofindthatIhavebeenabletoexplainstatisticswithaminimumamountofmathematicalformulasIwishtothankmywife,LanaStephens,forherpartinproducingabookthatisuptodateandforhelpingmewhenIneededhelp,understandingsomenursingconceptsthatIdidnotfullyunderstandSheisaformernursinginstructorandiscurrentlyanactiveNursePractitionerSheiswellawareoftheneedthatnurseshaveformathematicsandstatisticsIwishtothankmygoodfriendandlongtimetechnicalpartner,StanleyWilemanHewastherewhenIneededtoscanlabelsorpicturesofsyringestoincorporateintothebookIalsowishtothankDeidreWallofBectonDickinsonandCompanyfortherighttousetheirpicturesof=,=,andccsyringesIwishtothankJamieStokeratGlaxoSmithKlineforherhelpinsecuringlabelstobeusedinthebookIwishtothankKarenMcCannatMerckCo,Inc,forherhelpinsecuringlabelstobeusedinthebookThelabelsfortheproductsPrinivil,Vioxx,andZocorarereproducedwithpermissionofMerckCo,Inc,copyrightownerIwishtothankTiffanyTrunkoatPfizer,Inc,forherhelpinsecuringlabelstobeusedinthebookThelabelsarereproducedwithpermissionofPfizer,IncIwishtothankMicaelaTanesofEliLilly,Inc,forherhelpinsecuringlabelstobeusedinthebookIwishtothankMinitabforpermissiontoincludeoutputinthebookMINITABTMisatrademarkofMintab,Inc,intheUnitedStatesandothercountiesandisusedhereinwiththeowner’spermissionMinitabmaybereachedatwwwminitabcomorthefollowingaddress:vMinitabIncEnterpriseDriveStateCollege,PALARRYJSTEPHENSLANACSTEPHENSviPREFACETOTHESECONDEDITIONPREFACETOTHEFIRSTEDITIONThisbookisanintroductiontothemathematicsneededbythenurseinmodernclinicalpracticeItwillbeuseful()asaselfreviewtextforthosepreparingfornursinglicensingexaminationsor()asaclassroomoradjuncttextforacourseinnursingmathematicsThebookconsistsoftwopartsThefirstpartisareviewofbasicarithmetic,andtheseconddiscussesnursingapplicationsAfeatureofthisbookistheuseofaparticularlyeasyapproachtothesolutionofproportionproblems,namely,dimensionalanalysisDimensionalanalysisiscommonlyusedinthephysicalsciencesandengineeringforproblemsinconversionofameasurementfromoneunittoanotherThisisthesamekindofproblemwhichthenursemustmasterinordertoconvertamedicationordertoaforminwhichitcanbeadministeredtoapatientThefirstthreechapterscomprisethearithmeticreviewThosewhohaveagoodfoundationinarithmeticcanbegindirectlywiththesecondpartofthebookwhichstartswithChapteronsystemsofmeasurementandthemethodofdimensionalanalysisAthoroughgraspofthischapterisnecessarytounderstandtheremainingchaptersonnursingapplicationsAfurtherfeatureofthisbookistheinclusionofmaterialontheuseofthehandheldelectroniccalculatortoperformdosagecalculationsEachchaptercontainsexamplestoillustratethematerialunderdiscussionInaddition,eachchaptercontainsalargecollectionofsolvedproblemswhichareaccompaniedbydetailedsolutionstoeachproblem,andacollectionofsupplementaryproblems,answerstoallofwhicharesuppliedIwouldliketothankmywife,RuthNelson,RN,forhersupportandprofessionaladviceduringthewritingofthisbook,MorikoNishiuraforproofreadingthemathematics,andMelissaScholz,RN,forprofessionaladviceIwouldalsoliketoexpressmyappreciationformuchhelpandvaluedadvicetoProfessorEJDickasonoftheNursingDepartmentofQueensboroughCommunityCollege,andtomyeditors,KarlWeberandJeffMcCartneyEIZONISHIURAviiThispageintentionallyleftblankCONTENTSCHAPTERWholeNumberArithmeticNumberTheBaseTenSystemReadingNumeralsExpandedFormTheFundamentalOperationsOrderofOperations(forAdditionandMultiplication)AdditionofWholeNumbersSubtractionofWholeNumbersMultiplicationofWholeNumbersDivisionofWholeNumbersDivisorsandPrimeNumbersTheGreatestCommonDivisor(GCD)TheLeastCommonMultiple(LCM)CHAPTERWorkingwithFractionsTheMeaningofFractionsEquivalentFractionsReducingFractionsBuildingUpFractionsMultiplicationofFractionsDivisionofFractionsComplexFractionsAdditionandSubtractionofFractionswithaCommonDenominatorTheLeastCommonDenominator(LCD)AdditionandSubtractionofFractionswithDifferentDenominatorsMixedNumbersCalculationswithMixedNumbersComparingFractionsCHAPTERDecimalNumeralsDecimalNotationRoundingDecimalNumeralsAdditionandSubtractionofDecimalsixFormoreinformationaboutthistitle,clickhereCopyright,byTheMcGrawHillCompanies,IncClickHereforTermsofUseMultiplicationofDecimalsDivisionofDecimalsMultiplyingandDividingbyPowersofTenProblemsInvolvingDecimalsandFractionsComparingDecimalNumeralsCHAPTERMetric,Apothecary,andHouseholdMeasurementsDimensionalAnalysisWeightandVolumeTheMetricSystemTheApothecarySystemRomanNumeralsTheHouseholdSystemRatiosDimensionalAnalysisMetricConversionsConversionsbetweenSystemsCHAPTEROralMedicationConvertingMedicalDosagesOralMedicationinSolidFormOralMedicationinLiquidFormReconstitutingPowdersorCrystalstoLiquidFormCHAPTERParenteralDrugAdministrationDrugsAdministeredbyInjectionInjectablesinPowderorCrystalFormIntravenousInfusionInsulinAdministrationCHAPTERPediatricDosagesDosagesBasedonBodyWeightDosagesBasedonBodySurfaceAreaCHAPTERPercentagesPercentageChangingPercentagestoEquivalentFractionsChangingPercentagestoEquivalentDecimalNumeralsChangingDecimalNumeralstoEquivalentPercentagesChangingFractionstoEquivalentPercentagesPercentageofaNumberFindingthePercentageGiventhePartandtheBasexCONTENTSFindingthePartGiventhePercentageandtheBaseFindingtheBaseGiventhePercentageandthePartPercentageStrengthofSolutionsCHAPTERUsingtheElectronicCalculatorCalculatorsforNursingElementaryCalculationsExtendedCalculationsWorkingwithFractionsontheCalculatorDosageCalculationsThePercentKeyCHAPTERStatisticsforNursesStatisticsforNursingBarChartsandPieChartsforCategoricalDataHistogramsandDotPlotsforNumericalDataNumericalMeasuresforDescribingNumericalDataPropertiesofProbabilityandtheBinomialDistributionTheNormalDistributionPopulationandSampleEstimatingPopulationMeansandPercentagesTestingHypothesesaboutMeansandPopulationPercentagesAPPENDIXATemperatureConversionsAPPENDIXBSomeCommonlyUsedMedicalSymbolsandAbbreviationsINDEXCONTENTSxiCHAPTERWholeNumberArithmeticNUMBERCountingistheprocessusedtoanswerthequestion:HowmanyThenumbersusedforcounting‘‘one,two,three,four,five,’’andsoonarecalledthenaturalnumbersThesetofnaturalnumbers,togetherwiththenumber‘‘zero,’’iscalledthesetofwholenumbersNumbersmayberepresentedeitherbywordsorbysymbolscallednumeralsTherearemanysystemsofrepresentingwholenumbersbynumerals,ofwhichthemostcommonlyusedisthebasetensystemInthissystemthewholenumbersarewrittenas,,,,,,,,,,,,,andsoonTHEBASETENSYSTEMInthebasetensystemthefirsttenwholenumbers,,,,,,,,,areusedasdigitsAllotherwholenumbersarewrittenintermsofthesedigitsNumeralsareclassifiedaccordingtohowmanydigitstheycontainThus,thefirsttennumeralsarecalledsingledigitnumeralsOntheotherhand,isatwodigitnumeralsinceitcontainstwodigitssimilarly,isathreedigitnumeralAnynumeralwithmorethanonedigitiscalledamultipledigitnumeralThus,andaremultipledigitnumeralsThedigitsinabasetennumeraltellhowmany‘‘ones,’’‘‘tens,’’‘‘hundreds,’’andsoon,thenumbercontainsForexample,thenumberofthingsinthecollectionontheleftinFigisrepresentedbythenumeral,sincethecollectioncanbeseparatedintogroupsoftenplusones,asontherightSimilarly,thenumberofthingsinFigisrepresentedbythenumeralsinceitconsistsofgroupsofahundred,plusgroupsoften,plusonesAsthesetwoexamplesshow,thedigitsofanumeralareassignedplacevaluesaccordingtowheretheystandinthenumeralbythefollowingscheme:FigCopyright,byTheMcGrawHillCompanies,IncClickHereforTermsofUseThedigitfarthesttotherighthasplacevalueoneProceedingtotheleft,theplacevalueofeachdigitistentimestheplacevalueofthedigitimmediatelytotherightSincethedigitfarthesttotherighthasplacevalueone,theseconddigitfromtherighthasplacevalueten(tentimesone),thethirddigitfromtherighthasplacevalueahundred(tentimesten),thefourthdigitfromtherighthasplacevalueathousand(tentimesahundred),andsoonFigureillustratestheseplacevaluesThenumeral,showninthefigurehastenthousands,thousands,hundreds,tens,andonesEXAMPLEGivetheplacevaluesofeachdigitinthefollowingnumeralsandtellhowmanyones,tens,hundreds,andsoonthenumbercontains:(a)(b)(c)(a)ThehasplacevaluetenandthehasplacevalueoneThereforecontainstensandone(b)Thehasplacevalueahundred,thehasplacevalueten,andthehasplacevalueoneThereforecontainshundreds,tens,andones(orsimplyhundredsandones)(c)Thehasplacevalueathousand,thefirsthasplacevalueahundred,thesecondhasplacevalueten,andthethirdhasplacevalueoneThereforecontainsthousands,hundreds,tens,andones(orsimplythousands)READINGNUMERALSNotethattheplacevaluesinFigareseparatedintogroupsofthreeStartingfromtheright,thefirstgroupconsistsoftheones,tens,andhundredsthesecondgroupconsistsofthethousands,tenthousands,andhundredthousandsthethirdgroupconsistsofthemillions,tenmillions,andhundredmillionsandsoonInpractice,theuseofcommastoseparatedigitsinanumeralintogroupsofthreeaidsinreadingthenumberEXAMPLEReadthenumbers(a),(b),,(c),,,ThecommasmakeiteasiertoseewhattheplacevalueoftheleftmostdigitisthousandsFigFigPlacevaluesofbasetendigits!WHOLENUMBERARITHMETICCHAP(a)Read:twelvethousand,fourhundredtwentymillionsthousands(b)Read:onemillion,threehundredthousand,onehundredninetybillionsmillions(c)Read:fourbillion,threehundredmillionEXAMPLEWritethefollowingnumbersasbasetennumerals(a)Fivehundredseventythousand(b)Fourteenmillion,sixhundredthousand(c)Twobillion,threehundredeightymillion(a),(b),,(c),,,EXPANDEDFORMWhenanumberiswrittentoshowhowmanyones,tens,hundreds,andsoonthatitcontains,itissaidtobeinexpandedformForexample:hundredsþtensþonesSincehundredtensonesthesamenumbercanalsobewrittenþþThisalsoiscalledexpandedformEXAMPLEWritethefollowingnumbersinexpandedforminbothways:(a)(b)(c)(d),(a)tensþonesþ(b)hundredsþtensþoneþþ(c)thousandsþhundredsþtenþonesþþþ(d)tenthousandþthousandsþhundredsþonesþþþInthelastcase,notethatthetenswasnotwrittenOnlynonzerodigitsneedbeexpressedwhenanumberiswritteninexpandedform!!!!CHAPWHOLENUMBERARITHMETICTHEFUNDAMENTALOPERATIONSThefourfundamentaloperationsofarithmeticareaddition(þ),subtraction(),multiplication(),anddivision()SomeofthepropertiesofandproceduresforperformingthesecalculationswillnowbediscussedORDEROFOPERATIONS(FORADDITIONANDMULTIPLICATION)Whenaseriesofadditionsand=ormultiplicationsisperformed,theorderinwhichtheseoperationsarecarriedoutisasfollowsInaseriesofadditions,theadditionsareperformedinorderfromlefttorightForexample:þþþþþðFirstaddþ

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