drug math for nurses dimensional analysis for meds junior level i summer 2011

Drug Math For Drug Math For NursesNurses

Dimensional Analysis for Dimensional Analysis for MedsMeds

Junior Level IJunior Level I

Summer 2011Summer 2011

ObjectivesObjectives

• At the conclusion of this presentation, At the conclusion of this presentation, students will:students will:

• Have a general understanding of basic Have a general understanding of basic dimensional analysis calculations for dimensional analysis calculations for nursing drug mathnursing drug math

• Verbalize basic medical terms for drug Verbalize basic medical terms for drug math calculationsmath calculations

• Identify key points to review and Identify key points to review and understand before taking 1understand before taking 1stst Drug Math Drug Math Exam at UAMS College of NursingExam at UAMS College of Nursing

ResourcesResources

• LRC [5LRC [5thth floor of library—Ed II) floor of library—Ed II)– Computer Assisted Instruction (CAI) programs Computer Assisted Instruction (CAI) programs

available in the LRC during LRC hoursavailable in the LRC during LRC hours

• www.atitesting.com - My E Learning - - My E Learning - Tutorials - Meds Made EasyTutorials - Meds Made Easy

UAMS College of Nursing UAMS College of Nursing Drug Math Examination Drug Math Examination

PolicyPolicyBasicsBasics

• Students are required to take the drug math exam prior to Students are required to take the drug math exam prior to each course each course with a clinical component

• Students must score a minimum of 90% to pass the examStudents must score a minimum of 90% to pass the exam• 3 opportunities to pass3 opportunities to pass

– 11stst two (2) attempts are computerized and proctored in the two (2) attempts are computerized and proctored in the LRC (5LRC (5thth floor of Library) during normal business hours floor of Library) during normal business hours

– If you do not score 90% or above on Exam 2, you must If you do not score 90% or above on Exam 2, you must remediate with the Drug Math Coordinator prior to taking remediate with the Drug Math Coordinator prior to taking exam 3 (Notify the Drug Math Coordinator immediately after exam 3 (Notify the Drug Math Coordinator immediately after failing exam 2 to arrange remediation; failing exam 2 to arrange remediation; [email protected])[email protected])

– 33rdrd attempt, if necessary, is arranged with the appropriate attempt, if necessary, is arranged with the appropriate Drug Math CoordinatorDrug Math Coordinator

• Practice Exams may be taken at home or in the LRC during Practice Exams may be taken at home or in the LRC during normal hoursnormal hours

Metric ConversionsMetric Conversions

• You must be able to read the problemYou must be able to read the problem– Know the terminology and abbreviations usedKnow the terminology and abbreviations used

Metric & International Metric & International System (SI) TermsSystem (SI) Terms

• L = literL = liter• mL = millilitermL = milliliter• cc = cubic centimetercc = cubic centimeter• tsp = teaspoontsp = teaspoon• kg = kilogramkg = kilogram• g = gramg = gram• mg = milligrammg = milligram• mcg = microgrammcg = microgram• cm = centimetercm = centimeter• mEq = milliequivalentmEq = milliequivalent• gtt = dropgtt = drop

• PO = by mouthPO = by mouth

Basic ConversionsBasic Conversions

• 1 mL = 1 cc1 mL = 1 cc• 1 ounce = 30 mL or 30 cc1 ounce = 30 mL or 30 cc• 1 tablespoon = 15 mL or 15 cc1 tablespoon = 15 mL or 15 cc• 1 teaspoon (tsp) = 5 mL or 5 cc1 teaspoon (tsp) = 5 mL or 5 cc• 3 teaspoons (tsp) = 1 tablespoon3 teaspoons (tsp) = 1 tablespoon• 1 liter (L) = 1000 mL or 1000 cc1 liter (L) = 1000 mL or 1000 cc

Basic ConversionsBasic Conversions

• 1 kilogram (kg) = 2.2 pounds1 kilogram (kg) = 2.2 pounds

Medical Terms for Medical Terms for Medication Administration Medication Administration

TimesTimes• Q D = Every day (once per day)Q D = Every day (once per day)• BID = Twice dailyBID = Twice daily• TID = Three times per dayTID = Three times per day• QID = Four times per dayQID = Four times per day• Q HS = At bedtime (once per day)Q HS = At bedtime (once per day)• ac = before mealsac = before meals• pc = after mealspc = after meals

Relative Value of Relative Value of DecimalsDecimals

• Values on the left side of the decimal are Values on the left side of the decimal are increasing in valueincreasing in value

100 is larger than 10.00100 is larger than 10.00

• Values on the right side of the decimal are Values on the right side of the decimal are decreasing in valuedecreasing in value

0.1 is larger than 0.010.1 is larger than 0.01

Relative Value of Relative Value of DecimalsDecimals

1 2 3 4 . 5 6 7 81 2 3 4 . 5 6 7 8

Thousands

Hundreds

Tens

OnesTenths

Hundredths

Thousandths

Ten Thousandths

UAMS Rounding RulesUAMS Rounding Rulesml or cc:ml or cc: Tablets:Tablets:

If the answer is < 1cc (or ml) then round to the nearest

100th.Ex: 0.376 = 0.38 cc (or ml)

If the answer is > 1cc (or ml) then round to the nearest

10th.Ex: 1.57 = 1.6 cc (or ml)

Tablets, as a rule, can only be given whole or broken in half. Round to the nearest

half (0.5)Ex: 1.45 = 1.5 tablets 1.2 =

1 tablet

Round at the end of the problem, when you get to the answer (exception iswhen you’re converting pounds to kilograms (kg)) then you should roundto the nearest tenth as soon as you convert, then complete the problem(2.345 = 2.4)

UAMS Rounding RulesUAMS Rounding Rules

Rounding RulesRounding Rules

Basic Rounding:Basic Rounding: Remember:Remember:

If the number is 5 then round up. Ex: 1.57 = 1.6 1.45 = 1.5

0.686 = 0.69If the number is < 5 then round

down. Ex: 0.543 = 0.54

Round at the end of the problem.

The exception to this rule is when you are converting pounds to Kgs. Always convert and round to the nearest 10th and then complete the problem.

Converting pounds and kilograms:Converting pounds and kilograms:

Round to the nearest 10th.Ex: 120 pounds = 54.54 or 54.5 Kg

UAMS Rounding RulesUAMS Rounding Rules

• Basically it means, when you’re working a Basically it means, when you’re working a problem, don’t forget to round your answer problem, don’t forget to round your answer at the end (when you get your answer) at the end (when you get your answer) The computer is very specific and will count you wrong if you round wrong!!

• 0.345 mL = 0.35 mL (answer is < 1 mL)0.345 mL = 0.35 mL (answer is < 1 mL)• 1.345 mL = 1.4 mL (answer is > 1 mL)1.345 mL = 1.4 mL (answer is > 1 mL)• 0.99 mL = 0.99 mL (answer is < 1 mL)0.99 mL = 0.99 mL (answer is < 1 mL)• 0.995 mL = 1 mL (answer is 1 mL or greater)0.995 mL = 1 mL (answer is 1 mL or greater)

Basic Math ReviewBasic Math Review

• FractionsFractions

11 (numerator)(numerator)

--------

44 (denominator)(denominator)

Convert Fraction to Convert Fraction to DecimalDecimal

1 ____ 0.25--- = 4 ) 1 = 4 ) 1.00 4 8

20 20 0

Convert Fraction to Convert Fraction to DecimalDecimal

1 0.3333--- = 3 ) 1.0000 3 9

10 9 10 9

10 9 10 infinite

Convert Pounds to Convert Pounds to Kilograms (kg)Kilograms (kg)

• You are caring You are caring for a patient for a patient that weighs 73 that weighs 73 pounds. How pounds. How many kg does many kg does this person this person weigh? _______weigh? _______


• You are caring for a patient that You are caring for a patient that weighs 73 pounds. How many kg weighs 73 pounds. How many kg does this person weigh? _______does this person weigh? _______

• We know 1 kg = 2.2 poundsWe know 1 kg = 2.2 pounds


• You are caring for a patient that You are caring for a patient that weighs 73 pounds. How many kg does weighs 73 pounds. How many kg does this person weigh? this person weigh? ____33.233.2 __ __

• We know 1 kg = 2.2 poundsWe know 1 kg = 2.2 pounds

• 73 divided by 2.2 = 33.181818 = 33.2 73 divided by 2.2 = 33.181818 = 33.2 kgkg

round to nearest tenthround to nearest tenth


HintsHints

• When you convert pounds (larger number) to When you convert pounds (larger number) to kilograms (smaller number) your answer will kilograms (smaller number) your answer will always be smalleralways be smaller– 100 pounds (divided by) 2.2 kg/pound = 45.5 kg100 pounds (divided by) 2.2 kg/pound = 45.5 kg

• When you convert kilograms (smaller When you convert kilograms (smaller number) to pounds you need to multiply; number) to pounds you need to multiply; your answer will always be largeryour answer will always be larger– 10 kg X 2.2 pounds/kg = 22 pounds10 kg X 2.2 pounds/kg = 22 pounds

Reading Drug LabelsReading Drug Labels• Drug name will be Drug name will be

availableavailable– GenericGeneric– TradeTrade

• Container sizeContainer size• Concentration (unit of Concentration (unit of

measure)measure)• Lot numberLot number• Expiration dateExpiration date• Additional InformationAdditional Information

– ManufacturerManufacturer– Safety Precautions (but not Safety Precautions (but not

always)always)

Reading Drug LabelsReading Drug Labels

• Find the concentration (unit of measure) Find the concentration (unit of measure) of the drugof the drug– How many mg is in each tablet?How many mg is in each tablet?– How many mg is in how many mL of the How many mg is in how many mL of the

solution?solution?

– ExampleExample• The drug is supplied as 750 mg per 5 mLThe drug is supplied as 750 mg per 5 mL• The available dosage strength is 1 gram in 3.5 mLThe available dosage strength is 1 gram in 3.5 mL• Pharmacy sends 325 mg tabletsPharmacy sends 325 mg tablets• The drug available is 500 mg per tabletThe drug available is 500 mg per tablet


• Sometimes, you may be confused by Sometimes, you may be confused by a question that gives you “extra” a question that gives you “extra” information, like telling you how information, like telling you how large the container islarge the container is– ExampleExample

• The nurse has a 500 mL bottle or Drug A at The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoona strength of 30 mg per teaspoon

• What does this mean???What does this mean???


• The nurse has a 500 mL bottle or Drug A at a The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoonstrength of 30 mg per teaspoon

• What does this mean?What does this mean?– It means you have a bottle that contains 500 mL of It means you have a bottle that contains 500 mL of

Drug ADrug A– Each teaspoon (5 mL) contains 30 mg of Drug AEach teaspoon (5 mL) contains 30 mg of Drug A– So, the entire bottle contains 3000 mg of Drug ASo, the entire bottle contains 3000 mg of Drug A

• 500 mL (divide by) 5 mL = 100 X 30 mg = 3000 500 mL (divide by) 5 mL = 100 X 30 mg = 3000 mgmg

Reading Drug LabelsReading Drug Labels• For dosage calculation, you need to be able to find For dosage calculation, you need to be able to find

the concentration (unit of measure) even when more the concentration (unit of measure) even when more information is given than neededinformation is given than needed– Take the same example Take the same example

• The nurse has a 500 mL bottle or Drug A at a strength of 30 mg The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoonper teaspoon

• The concentration (unit of measure) is The concentration (unit of measure) is 30 mg per teaspoon; the 500 mL is “extra” information that you ; the 500 mL is “extra” information that you don’t need in order to calculate how many mL to givedon’t need in order to calculate how many mL to give

– Remember, 1 tsp = 5 mL, so you have Remember, 1 tsp = 5 mL, so you have 30 mg/5 mL

Dimensional AnalysisDimensional Analysis

StepsSteps

• Find the unit of measure being calculated Find the unit of measure being calculated and write it, then put an equal = signand write it, then put an equal = sign– This guides you so you know where to put This guides you so you know where to put

each piece of information; Very important stepeach piece of information; Very important step

• ExampleExample

mL =mL =tab =tab =


22ndnd step step• Find what you have on hand [the Find what you have on hand [the

concentration of drug (unit of concentration of drug (unit of measure)]measure)]– ExampleExample

• 100 mg per 5 mL100 mg per 5 mL• 0.125 mg per 3.5 mL0.125 mg per 3.5 mL• 500 mg per tablet500 mg per tablet• 1 gram / 10 mL1 gram / 10 mL• 2 grams / 1 ounce2 grams / 1 ounce


22ndnd step continued step continued• This is placed in the first spot right of the This is placed in the first spot right of the

equal sign as a ratio (clinical ratio)equal sign as a ratio (clinical ratio)• The numerator must match the unit of The numerator must match the unit of

measure being calculatedmeasure being calculated– ExampleExample

5 mL5 mLmL = ---------mL = ---------

100 mg100 mg

numerator

denominator


33rdrd step step• The unit of measure in each denominator The unit of measure in each denominator

must be matched in the successive must be matched in the successive numerator enterednumerator entered– ExampleExample

• If the doctor orders 50 mg of Drug A (previous slide). If the doctor orders 50 mg of Drug A (previous slide). The concentration was 100 mg/5 mLThe concentration was 100 mg/5 mL

5 mL5 mL 50 mg 50 mg

mL = ----------mL = ---------- XX ----------------------

100 mg100 mg

numerator

denominator

successive numerator


Final StepFinal Step• Cancel out common denominator & Cancel out common denominator &

numeratornumerator• Cancel out common terms (mg, gram & Cancel out common terms (mg, gram &

so on)so on)– ExampleExample

5 mL5 mL 50 mg 50 mgmL = ----------mL = ---------- XX ----------------------

100 mg100 mg2

1


• Now, do the math to get your Now, do the math to get your answeranswer– Remember your rounding rulesRemember your rounding rules

5 mL5 mL 50 mg 5 50 mg 5

mL = ----------mL = ---------- X ---------X --------- = ---- = = ---- = 2.5 mL2.5 mL

100 mg 2100 mg 2

1

2


• Prepare a 500 mg dose of Prepare a 500 mg dose of Vancomycin from an available Vancomycin from an available solution of 1000 mg per 3 mL.solution of 1000 mg per 3 mL.

3 mL3 mL 500 mg 500 mg

mL = ------------mL = ------------ X ----------X ---------- = =

1000 mg 1000 mg


3 mL3 mL 500 mg 500 mg

mL = ------------mL = ------------ X ----------X ---------- = =

1000 mg 1000 mg

11stst reduce the common numerator & reduce the common numerator & denominatordenominator

1

2


3 mL3 mL 500 mg 500 mg

mL = ------------mL = ------------ X ----------X ---------- = =

1000 mg 1000 mg

next, cancel out “like terms”next, cancel out “like terms”

1

2


3 mL3 mL 500 mg 500 mg 3 3

mL = ------------mL = ------------ X ----------X ---------- = ---- = = ---- = 1.5 mL1.5 mL

1000 mg 21000 mg 2

Last, do the math!Last, do the math!

1

2


• If you need to do a metric conversion, it is If you need to do a metric conversion, it is added to the equation in the middleadded to the equation in the middle– ExampleExample

1 tab1 tab 500 mg 500 mg

tab = --------- X -----------tab = --------- X -----------

1 gram1 gram

As you can see, we can’t cancel out any “like As you can see, we can’t cancel out any “like terms”terms”


• Metric ConversionMetric Conversion

1 tab1 tab 500 mg 500 mg

tab = --------- X -----------tab = --------- X -----------

1 gram1 gram

• We know that 1 gram = 1000 mg, so we can put We know that 1 gram = 1000 mg, so we can put this into the equation (in the middle)this into the equation (in the middle)

1 gram1000 mg



1 tab1 tab 1 gram 500 mg1 gram 500 mg

tab = --------- X ----------- X ----------- =tab = --------- X ----------- X ----------- =

1 gram 1000 mg1 gram 1000 mg



1 tab1 tab 1 gram 500 mg1 gram 500 mgtab = --------- X ----------- X ----------- =tab = --------- X ----------- X ----------- = 1 gram 1000 mg1 gram 1000 mg

Now we can cancel out and reduce Now we can cancel out and reduce commonscommons

1

2

Dimensional AnalysisDimensional Analysis• Metric ConversionMetric Conversion

1 tab1 tab 1 gram 500 mg 1 1 gram 500 mg 1

tab = --------- X ----------- X ----------- = --- = 0.5 tab = --------- X ----------- X ----------- = --- = 0.5 tabtab

1 gram 1000 mg 2 1 gram 1000 mg 2

Last, do the math for your answer!!Last, do the math for your answer!!

1

2

Insulin AdministrationInsulin Administration– Insulin is always ordered in unitsInsulin is always ordered in units– Do not abbreviate units as U, it must be Do not abbreviate units as U, it must be

spelled out to prevent medication errorsspelled out to prevent medication errors– Insulin is supplied in U-100 dosesInsulin is supplied in U-100 doses

• 1 unit = 0.01 mL1 unit = 0.01 mL• 10 units = 0.1 mL or 0.10 mL10 units = 0.1 mL or 0.10 mL• 100 units = 1 mL100 units = 1 mL

– You must use specially marked syringes [they You must use specially marked syringes [they are usually orange color] to give insulin (they are usually orange color] to give insulin (they are called insulin syringes); do not draw up are called insulin syringes); do not draw up insulin in a standard syringeinsulin in a standard syringe

drug math for nurses dimensional analysis for meds junior level i summer 2011

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