1. Drug Math For Nurses Dimensional Analysis for Meds Junior Level I Summer 2011

2. Objectives At the conclusion of this presentation, students will:At the conclusion of this presentation, students will: Have a general understanding of basic dimensional analysis calculations for nursing drug mathHave a general understanding of basic dimensional analysis calculations for nursing drug math Verbalize basic medical terms for drug math calculationsVerbalize basic medical terms for drug math calculations Identify key points to review and understand before taking 1 st Drug Math Exam at UAMS College of NursingIdentify key points to review and understand before taking 1 st Drug Math Exam at UAMS College of Nursing

3. Resources LRC [5 th floor of library—Ed II)LRC [5 th floor of library—Ed II) –Computer Assisted Instruction (CAI) programs available in the LRC during LRC hours www.atitesting.com - My E Learning - Tutorials - Meds Made Easywww.atitesting.com - My E Learning - Tutorials - Meds Made Easywww.atitesting.com

4. UAMS College of Nursing Drug Math Examination Policy Basics Students are required to take the drug math exam prior to each courseStudents are required to take the drug math exam prior to 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 –1 st two (2) attempts are computerized and proctored in the LRC (5 th floor of Library) during normal business hours –If you do not score 90% or above on Exam 2, you must remediate with the Drug Math Coordinator prior to taking exam 3 (Notify the Drug Math Coordinator immediately after failing exam 2 to arrange remediation; martinwatsonalicel@uams.edu) –3 rd attempt, if necessary, is arranged with the appropriate Drug Math Coordinator Practice Exams may be taken at home or in the LRC during normal hoursPractice Exams may be taken at home or in the LRC during normal hours

5. Metric Conversions You must be able to read the problemYou must be able to read the problem –Know the terminology and abbreviations used

6. Metric & International System (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

7. Basic 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

8. Basic Conversions 1 kilogram (kg) = 2.2 pounds1 kilogram (kg) = 2.2 pounds

9. Medical Terms for Medication Administration Times 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

10. Relative Value of Decimals Values on the left side of the decimal are increasing in valueValues on the left side of the decimal are increasing in value 100 is larger than 10.00 Values on the right side of the decimal are decreasing in valueValues on the right side of the decimal are decreasing in value 0.1 is larger than 0.01

11. Relative Value of Decimals 1 2 3 4. 5 6 7 8 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten Thousandths

12. UAMS Rounding Rules ml or cc: 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 is when you’re converting pounds to kilograms (kg)) then you should round to the nearest tenth as soon as you convert, then complete the problem (2.345 = 2.4)

13. UAMS Rounding Rules Rounding Rules Basic Rounding: Remember: If the number is  5 then round up. Ex: 1.57 = 1.6 1.45 = 1.5 0.686 = 0.69 If 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: Round to the nearest 10th. Ex: 120 pounds = 54.54 or 54.5 Kg

14. UAMS Rounding Rules Basically it means, when you’re working a problem, don’t forget to round your answer at the end (when you get your answer)Basically it means, when you’re working a problem, don’t forget to round 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)

15. Basic Math Review FractionsFractions 1(numerator) 1(numerator)---- 4(denominator) 4(denominator)

16. Convert Fraction to Decimal 1 ____ 0.25 --- = 4 ) 1= 4 ) 1.00 4 8 20 0

17. Convert Fraction to Decimal 1 0.3333 --- =3 ) 1.0000 3 9 10 9 10 9 10 9 10 infinite

18. Convert Pounds to Kilograms (kg) You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______

19. Convert Pounds to Kilograms (kg) You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? _______ We know 1 kg = 2.2 poundsWe know 1 kg = 2.2 pounds

20. Convert Pounds to Kilograms (kg) You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? __33.2 __You are caring for a patient that weighs 73 pounds. How many kg does this person weigh? __33.2 __ We know 1 kg = 2.2 poundsWe know 1 kg = 2.2 pounds 73 divided by 2.2 = 33.181818 = 33.2 kg73 divided by 2.2 = 33.181818 = 33.2 kg round to nearest tenth

21. Convert Pounds to Kilograms (kg) Hints When you convert pounds (larger number) to kilograms (smaller number) your answer will always be smallerWhen you convert pounds (larger number) to kilograms (smaller number) your answer will always be smaller –100 pounds (divided by) 2.2 kg/pound = 45.5 kg When you convert kilograms (smaller number) to pounds you need to multiply; your answer will always be largerWhen you convert kilograms (smaller number) to pounds you need to multiply; your answer will always be larger –10 kg X 2.2 pounds/kg = 22 pounds

22. Reading Drug Labels Drug name will be availableDrug name will be available –Generic –Trade Container sizeContainer size Concentration (unit of measure)Concentration (unit of measure) Lot numberLot number Expiration dateExpiration date Additional InformationAdditional Information –Manufacturer –Safety Precautions (but not always)

23. Reading Drug Labels Find the concentration (unit of measure) of the drugFind the concentration (unit of measure) of the drug –How many mg is in each tablet? –How many mg is in how many mL of the solution? –Example 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

24. Reading Drug Labels Sometimes, you may be confused by a question that gives you “extra” information, like telling you how large the container isSometimes, you may be confused by a question that gives you “extra” information, like telling you how large the container is –Example The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoonThe nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon What does this mean???What does this mean???

25. Reading Drug Labels The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoonThe nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon What does this mean?What does this mean? –It means you have a bottle that contains 500 mL of Drug A –Each teaspoon (5 mL) contains 30 mg of Drug A –So, the entire bottle contains 3000 mg of Drug A 500 mL (divide by) 5 mL = 100 X 30 mg = 3000 mg500 mL (divide by) 5 mL = 100 X 30 mg = 3000 mg

26. Reading Drug Labels For dosage calculation, you need to be able to find the concentration (unit of measure) even when more information is given than neededFor dosage calculation, you need to be able to find the concentration (unit of measure) even when more information is given than needed –Take the same example The nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoonThe nurse has a 500 mL bottle or Drug A at a strength of 30 mg per teaspoon The concentration (unit of measure) is ; the 500 mL is “extra” information that you don’t need in order to calculate how many mL to giveThe concentration (unit of measure) is 30 mg per teaspoon; the 500 mL is “extra” information that you don’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

27. Dimensional Analysis Steps Find the unit of measure being calculated and write it, then put an equal = signFind the unit of measure being calculated and write it, then put an equal = sign –This guides you so you know where to put each piece of information; Very important step ExampleExample mL = tab =

28. Dimensional Analysis 2 nd step Find what you have on hand [the concentration of drug (unit of measure)]Find what you have on hand [the concentration of drug (unit of measure)] –Example 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

29. Dimensional Analysis 2 nd step continued This is placed in the first spot right of the equal sign as a ratio (clinical ratio)This is placed in the first spot right of the equal sign as a ratio (clinical ratio) The numerator must match the unit of measure being calculatedThe numerator must match the unit of measure being calculated –Example 5 mL 5 mL mL = --------- 100 mg 100 mg numerator denominator

30. Dimensional Analysis 3 rd step The unit of measure in each denominator must be matched in the successive numerator enteredThe unit of measure in each denominator must be matched in the successive numerator entered –Example If the doctor orders 50 mg of Drug A (previous slide). The concentration was 100 mg/5 mLIf the doctor orders 50 mg of Drug A (previous slide). The concentration was 100 mg/5 mL 5 mL 50 mg 5 mL 50 mg mL = ----------X----------- 100 mg numerator denominator successive numerator

31. Dimensional Analysis Final Step Cancel out common denominator & numeratorCancel out common denominator & numerator Cancel out common terms (mg, gram & so on)Cancel out common terms (mg, gram & so on) –Example 5 mL 50 mg 5 mL 50 mg mL = ----------X----------- 100 mg 100 mg 2 1

32. Dimensional Analysis Now, do the math to get your answerNow, do the math to get your answer –Remember your rounding rules 5 mL 50 mg 5 5 mL 50 mg 5 mL = ----------X ---------= ---- = 2.5 mL 100 mg 2 100 mg 2 1 2

33. Dimensional Analysis Prepare a 500 mg dose of Vancomycin from an available solution of 1000 mg per 3 mL.Prepare a 500 mg dose of Vancomycin from an available solution of 1000 mg per 3 mL. 3 mL 500 mg 3 mL 500 mg mL = ------------X ---------- = 1000 mg 1000 mg

34. Dimensional Analysis 3 mL 500 mg 3 mL 500 mg mL = ------------X ---------- = 1000 mg 1000 mg 1 st reduce the common numerator & denominator 1 2

35. Dimensional Analysis 3 mL 500 mg 3 mL 500 mg mL = ------------X ---------- = 1000 mg 1000 mg next, cancel out “like terms” 1 2

36. Dimensional Analysis 3 mL 500 mg 3 3 mL 500 mg 3 mL = ------------X ---------- = ---- = 1.5 mL 1000 mg 2 1000 mg 2 Last, do the math! 1 2

37. Dimensional Analysis If you need to do a metric conversion, it is added to the equation in the middleIf you need to do a metric conversion, it is added to the equation in the middle –Example 1 tab 500 mg 1 tab 500 mg tab = --------- X ----------- 1 gram 1 gram As you can see, we can’t cancel out any “like terms”

38. Dimensional Analysis Metric ConversionMetric Conversion 1 tab 500 mg 1 tab 500 mg tab = --------- X ----------- 1 gram 1 gram We know that 1 gram = 1000 mg, so we can put this into the equation (in the middle)We know that 1 gram = 1000 mg, so we can put this into the equation (in the middle) 1 gram 1000 mg

39. Dimensional Analysis Metric ConversionMetric Conversion 1 tab1 gram 500 mg 1 tab1 gram 500 mg tab = --------- X ----------- X ----------- = 1 gram 1000 mg 1 gram 1000 mg

40. Dimensional Analysis Metric ConversionMetric Conversion 1 tab1 gram 500 mg 1 tab1 gram 500 mg tab = --------- X ----------- X ----------- = 1 gram 1000 mg 1 gram 1000 mg Now we can cancel out and reduce commons 1 2

41. Dimensional Analysis Metric ConversionMetric Conversion 1 tab 1 gram 500 mg 1 1 tab 1 gram 500 mg 1 tab = --------- X ----------- X ----------- = --- = 0.5 tab 1 gram 1000 mg 2 1 gram 1000 mg 2 Last, do the math for your answer!! 1 2

42. Insulin Administration –Insulin is always ordered in units –Do not abbreviate units as U, it must be spelled out to prevent medication errors –Insulin 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 are usually orange color] to give insulin (they are called insulin syringes); do not draw up insulin in a standard syringe