South Texas College Associate Degree in Nursing. RNSG 1262 Clinical 1. Math and Dosage Calculations Module

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1 South Texas College Associate Degree in Nursing RNSG 1262 Clinical 1 Math and Dosage Calculations Module Study this Module and answer all the practice questions. Show your computation and write the final answer on the space provided. Submit this pocket to your Clinical Instructor on the first day of school. Math and Dosage Calculations Module Level 1_rev _pjc Page 1

2 Table of Contents Page I. Arithmetic Needed for Dosage A. Fractions 3 B. Decimals 4 II. Common Calculations 6 III. IV. Systems of Measurement A. Metric System 7 B. Apothecary System 8 C. Household System 11 D. Other Conversions 1. Temperature Conversions Milliequivalent and Milliunit 19 Common Medical Abbreviations A. Time of Administration of Drugs Military Time: The 24-Hour Clock B. Routes of Administration of Drugs 22 C. Units of Measure 23 D. General V. Calculations of Oral Medications A. Oral Solids 24 B. Oral Liquids 26 VI. Calculations of Parenteral Medications A. Injections from a Liquid 29 B. Injections from Powders 32 C. Insulin Injections 34 VII. Dosages Based on Body Weight 35 Math and Dosage Calculations Module Level 1_rev _pjc Page 2

3 Module 1: Arithmetic Needed for Dosage A. Fractions A fraction indicates a portion of a whole number. Example: = 1 part of 4 parts, or 4 of the whole Mixed Numbers: When a whole number and a fraction are combined, the result is referred to as a mixed number. 5 5 Example: 1 = Reducing Fractions to the Lowest Terms: When calculating dosages, it is usually easier to work with fractions using the smallest possible numbers. To reduce a fraction to lowest terms, divide both the numerator and denominator by the largest non-zero whole number that will go evenly into both numerator and denominator. Example: 6 Reduce 12 to lowest terms 6 12 = = 1 2 Note: For tablets if the value is less than a whole number always write it in fraction. Example: Correct: 1 ½ tablets Wrong: 1.5 tablets Math and Dosage Calculations Module Level 1_rev _pjc Page 3

4 B. Decimals Decimal numbers are numeric values that include a whole number, a decimal point, and a decimal fraction. Whole Numbers Decimal Fractions T H T O d h u e n e s n r t o n n e c t d d h u d s s i s r m d d d d a e a e e e e n d l d s m m m m s p a a a a o l l l l i c i c i c i c i p p p p n l l l l t a a a a c c c c e e e e / / / / # # # # No trailing zero When writing decimals, eliminate unnecessary zeros at the end of the number to avoid confusion. The Joint Commission forbids the use of trailing zeros for medication orders or other medication-related documentation and cautions that, in such cases, the decimal point maybe missed when unnecessary zero is written. Example: Correct: 10 Wrong: 10.0 which can be misinterpreted as 100 if decimal point is not clear. Always place a leading zero Always write a zero to the left of the decimal point to emphasize that the number has a value less than 1. The Joint Commission s Official Do Not Use list prohibits writing a decimal fraction that is less than 1 without a leading zero. Example: Correct: 0.45 Wrong:.45 which can be misinterpreted as 45 if the decimal point is not clear or if the decimal point is overlooked. Math and Dosage Calculations Module Level 1_rev _pjc Page 4

5 Rounding Decimal Numbers Sometimes it is convenient to round an answer that is, to use an approximate answer rather than the exact one. Rounding Off To round off to the 1 st decimal place or 1 st decimal number do the following: Look at the digit after the 1 st decimal place (the number on the right or the number on the 2 nd decimal place). Because this digit (6) is 5 or more, round off by adding 1 to the number on the 1 st decimal place. Finally, drop all the digits after the 1 st decimal place. So, is approximated by 1.3 when rounded off to the 1 st decimal place/number. To round off to the 2 nd decimal place or 2 nd decimal number do the following: Look at the digit after the 2 nd decimal place (the number to the right or the number on the 3 rd decimal place). Because this digit (4) is less than 5, round off by leaving the 2 nd decimal digit alone. Finally, drop all the digits after the 2 nd decimal place. So, is approximated by 0.83 when rounded off to the 2 nd decimal place/number. Practice Exercises: st st 1. Round off to the 1 decimal place or 1 decimal number. nd nd 2. Round off to the 2 decimal place or 2 decimal number. 3. Round off to a whole number. Math and Dosage Calculations Module Level 1_rev _pjc Page 5

6 Module II: Common Dosage Calculations Methods Formula Method Step 1. Convert Step 2. Think Desired dose Step 3. Calculate: x Quantity = unknown Dose on hand Proportion Method Step 1. Convert Step 2. Think Step 3. Calculate: Dosage on hand Amount on hand = Dosage desired X Amount desired *Dimensional Analysis Method = *highly recommended method to use Step 1. Determine unit of measure for amount to give ratio for left side of equation Step 2. Think Step 3. Match unit of numerator of supply dosage with the unit of numerator of amount to give. Set up all other ratios so units cancel, leaving unit of amount to give. Calculate: Supply Desire Amount to give = x + conversion factors as needed Have Math and Dosage Calculations Module Level 1_rev _pjc Page 6

7 Module III: Systems of Measurement A. Metric System Unit Abbreviation Equivalents Weight Volume Length gram (base unit) milligram microgram kilogram liter (base unit) milliliter meter (base unit) centimeter millimeter g mg mcg kg L ml m cm mm 1 g = 1000 mg = mcg g = 1 mg = 1000 mcg g = mg = 1 mcg 1 kg = 1000 g 1 L = 1000 ml L = 1 ml 1 m = 100 cm = 1000 mm 0.01 m = 1 cm = 10 mm m = 0.1 cm = 1 mm Note: No commas on amounts at or above one thousand. Example: Correct: 1000 Wrong: 1,000 which the comma can be misinterpreted as a decimal point if not written legibly Practice Exercises: 1. Change to the designated equivalents. 76 mg = mcg 2. Change to the designated equivalents. 1.5L = ml 3. Change to the designated equivalents cm = mm Math and Dosage Calculations Module Level 1_rev _pjc Page 7

8 B. Apothecary System The style of apothecary notations includes: 1. The unit or abbreviation typically precedes the amount. Example: gr v 2. Lowercase Roman numerals are often used to express whole numbers Fractions are used to designate amounts less than 1. Example: gr, gr Symbol ss used to designate the fraction but, because this symbol can 2 easily be misinterpreted thus, it is no longer used. Arabic Number Roman Numeral Apothecary Notation 1 l i or l 2 ll ii or ll 4 lv iv 5 V v 9 lx ix 10 X x 15 XV xv 20 XX xx Equivalents: gr i = 60 mg or 65 mg Example # 1: Convert: 120 mg to gr Approximate equivalent: gr i = 60 mg. Conversion factor is 60 mg/gr THINK: Smaller Larger Divide 120 mg 60 mg/gr = gr 2 (Wrong) gr ii (Correct) Math and Dosage Calculations Module Level 1_rev _pjc Page 8

9 Example # 2: Order: phenobarbital gr ii PO q8h. On hand: phenobarbital 60 mg per tablet. What is the amount to administer? (Use gr i = 60 mg) 1 tab 60 mg gr ii 120? tab = x x = = 2 tabs 60 mg gr i 60 Practice Exercises: gr 1. Convert 2400 mg to grains. (Use gr i = 60 mg) mg 2. An order is for gr iii of medication. How many milligrams should the patient receive? (Use gr i = 65 mg) ml 3. Calculate the amount you will prepare for one dose. Order: atropine gr 1/100 IM on call to O.R Supply: atropine 0.4 mg/ml (Use gr i = 60mg) Math and Dosage Calculations Module Level 1_rev _pjc Page 9

10 ml 4. Order: morphine sulfate gr ¼ IM stat Supply: morphine sulfate 10 mg/ml How many milliliters of morphine would you administer? (Use gr i = 60 mg) 5. The physician ordered acetaminophen gr x PO q6h prn for mild to moderate pain. tab/s Stock available: A. acetaminophen 325 mg tab. B. acetaminophen 500 mg tab. Which tablet are you going to use A or B & how many tab/s are you going to administer? (Write both answers on the space provided.) Math and Dosage Calculations Module Level 1_rev _pjc Page 10

11 C. Household System The household unit is likely used by patient at home where hospital measuring devices are not usually available. You should be familiar with the household system of measurement so that you can explain take-home prescriptions to your patient. Equivalents Household Measures Metric Measures 1 t 5 ml 3 t 1 T 15 ml 2 T 1 fl oz 30 ml 1 cup 8 fl oz 240 ml 1 pint 2 cups or 16 fl oz 480 ml 1 lb 16 oz 2.2 lb 1 kg 1 in 2.54 cm 1 ft 12 in Practice Exercises: ml 1. The urinary output of a patient with an indwelling Foley catheter is 1.4 L. How many milliliters of urine are in the bag? Math and Dosage Calculations Module Level 1_rev _pjc Page 11

12 ml 2. What is the patient s total fluid intake in ml for the day if he had the following fluid intake? Breakfast = 8 oz. milk, 1 cup water Lunch = 4 oz. juice, 3 T medication, ½ cup water Dinner = 6 oz. soup, 12 oz soda, ½ cup water oz. 3. The patient drank 720 ml of the laxative agent Colyte. How many ounces of laxative did the patient drank? Example: A patient needs to drink 1.5 oz. of an elixir per day. How many teaspoons would be equivalent to this dose? 1 tsp 30 ml 1.5 oz 45? tsp. = x x = = 9 tsp. 5 ml 1 oz 5 Practice Exercises: tsp/s. 1. A patient is to take 5 ml of a medication. However, he will be using a teaspoon at home. The nurse instructed the patient that dose will be equivalent to tsp/s. Math and Dosage Calculations Module Level 1_rev _pjc Page 12

13 T 2. Order: Amoxil (amoxicillin) oral suspension 1tsp PO q8h. How many tablespoons of Amoxil (amoxicillin) will the patient receive in 3 full days? tsp 3. The order is indomethacin 75 mg PO daily in 3 divided doses. The label reads indomethacin 25 mg per 5 ml. How many teaspoons should you administer per dose? Practice Exercises 4 and 5 refers to this scenario. Scenario: A patient is given a prescription to take 15 ml of medication every 8 hours for 10 days. The patient will be using a household measuring device at home to measure the dose of medication. tsp/s 4. How many teaspoon/s of medication will the patient take in one day? bottles 5. If the medication is supplied in a 0.5 L bottle, how many bottles will the patient need to complete the 10 days of treatment? Math and Dosage Calculations Module Level 1_rev _pjc Page 13

14 Example: Adam is 6 feet 3 inches tall. What is his height in centimeters? 2.54 cm 12 in 6 ft+3 in 75 in? cm = x ( x ) = = cm 1 in ft Practice Exercises: mm 1. A tumor has a diameter of 2 inches. What is the diameter of the tumor measured in millimeters? cm 2. A patient is 5 feet 9 inches tall. Find the height of the patient in centimeters. (Round off your answer to the first decimal number/place.) in 3. A patient is 182 centimeters tall. Find the height of the patient in inches. (Round off your answer to the second decimal number/place.) Math and Dosage Calculations Module Level 1_rev _pjc Page 14

15 Example: Jennifer weighs 115 pounds 8 ounces. What is her weight in kilograms? 1 kg 115 lb + 8 oz 1 lb 0.5 lb 115.5? kg = x ( x ) = = 52.5 kg 2.2 lb 16 oz 2.2 Practice Exercises: lb 1. A woman weighs 75 kilograms. What is her weight in pounds? kg 2. Harold weighs 250 pounds now. If Harold goes on a diet and loses 30 pounds, then how many kilograms will he weigh? kg 3. An infant weighs 3400 grams. How much does this infant weigh in kilograms? Math and Dosage Calculations Module Level 1_rev _pjc Page 15

16 D. Other Conversions Temperature Conversions: The Fahrenheit scale establishes the freezing point of pure water at 32 degrees and the boiling point of pure water at 212 degrees. The Celsius scale establishes the freezing point of pure water at 0 degrees and the boiling point of pure water at 100 degrees. Conversion: Fahrenheit to Celsius, first subtract 32 and then divide the result by 1.8 ºC = Example: Convert 98.6 o F to degrees Celsius. ºC = ºC = = Therefore, 98.6 ºF = 37 ºC Practice Exercises: C 1. Convert 99.5 o F to degrees Celsius. C 2. Convert 97.2 o F to degrees Celsius. (Round off to the second decimal number.) Math and Dosage Calculations Module Level 1_rev _pjc Page 16

17 C 3. A mother brought her 6 yr old boy to the physician s office due to fever, with current temperature of F which is equivalent to C. (Round off to the first decimal number.) Practice Exercises 4 and 5, refers to this scenario. º Scenario: The state health department requires that certain medications be stored between 36 F º and 41 F. The refrigerator in the medication room has a Celsius thermometer. ºC 4. What should be the minimum temperature setting for the refrigerator in Celsius? (Round off to the second decimal number.) ºC 5. What should be the maximum temperature setting for the refrigerator in Celsius? Math and Dosage Calculations Module Level 1_rev _pjc Page 17

18 Conversion: Celsius to Fahrenheit, first multiply by 1.8 and then add 32 ºF = ºC x Example: Convert 37 ºC to ºF ºF = 1.8(37) + 32 ºF = ºF = 98.6 Therefore, 37 ºC = 98.6 ºF Practice Exercises: º F 1. Convert 38.6 ºC to degrees Fahrenheit. (Round off to the first decimal number.) º F 2. Convert 40 ºC to degrees Fahrenheit. º F 3. Convert 39.3 ºC to degrees Fahrenheit. (Round off to the first decimal number.) Math and Dosage Calculations Module Level 1_rev _pjc Page 18

19 International unit, unit, milliunit, and milliequivalent: Four other measurements maybe used to indicate quantity of medicine prescribed: international unit, unit, milliunit, and milliequivalent. It is not necessary to learn conversions for these units of measure because medications prescribed in these measurements are also prepared and administered in the same system. Example of medication measured in units Example of medication measured in milliequivalent / meq Math and Dosage Calculations Module Level 1_rev _pjc Page 19

20 Module IV: Common Medical Abbreviations A. Time of Drug Administration Sample Time ac = before meals = 0730, 1130, 1630 bid = twice a day = 1000, 1800 or 0900, 2100 hs = at bedtime, at hour of sleep = 2100 tid = three times a day = 1000, 1400, 1800 qid = four times a day = 1000, 1400, 1800, 2200 qh = every hour q2h = every 2 hours q3h = every 3 hours q4h = every 4 hours pc = after meals = 1000, 1400, 1800 prn = whenever needed, when necessary stat = immediately, at once Traditional Time/Conventional Time Military Time/ 24-Hour Clock Time 12:00 midnight or 12:00 AM 2400 or :10 AM :00 AM :00 AM :00 noon or 12:00 PM :00 PM :00 PM :00 PM 2300 Rules: Math and Dosage Calculations Module Level 1_rev _pjc Page 20

21 1. Traditional time and international time are the same hours starting with 1:00 AM or 0100 through 12:59 PM or Minutes after 12:00 AM and before 1:00 AM are 0001 through 0059 in international time. 3. Hours starting with 1:00 PM through 12:00 AM are 12:00 hours greater in international time. 4. International time is designated by a unique four-digit number without a colon. Example # 1: 1. 5:00 PM = 5: :00 = :35 AM= = = = 8:00 PM = = 12:05 AM Example # 2: The patient receives an initial dose of medicine at 12:00 PM while in the physician's office. The physician orders the medication to be taken every 6 hours. The patient should be told to take the next dose at (Use military time/24h clock time.) 1200 or 12:00 PM initial dose/1 st dose + 6 hrs for the next dose 1800 = the time for the next dose Practice Exercises: 1. Convert 11:39 PM to Military time. Practice Exercises 2 and 3, refers to this scenario. Math and Dosage Calculations Module Level 1_rev _pjc Page 21

22 Scenario: A patient was prescribed metronidazole 500 mg PO q 8h. The initial dose was taken at 8:00 AM. 2. At what time will the patient take the next dose? (Use Military time) 3. At what time will the patient take the 3 rd dose? (Military time/24-hour clock time) B. Route of Drug Administration HHN = Hand-held nebulizer ID = Intradermal IM = Intramuscular IV = Intravenous IVF = Intravenous Fluid IVPB = Intravenous Piggyback NGT = nasogastric tube PEG = percutaneous endoscopic gastrostomy po/po = by mouth pr/pr = per rectum SL = Sublingual Subcu = subcutaneous Supp = suppository Top = topical od = right eye os = left eye ou = both eyes C. Units of Measure Math and Dosage Calculations Module Level 1_rev _pjc Page 22

23 c = cup cm = centimeters ft = foot g = grams gr = grains in = inches kg = kilograms L = liters lb = pound m = meters mcg = micrograms meq = milliequivalents mg = milligrams ml = milliliters mm = millimeters oz = ounce pt = pint T /tbs = tablespoons t/tsp = teaspoons D. General cap = capsule ER = extended release gtt = drop NKA = no known allergy NPO = nothing by mouth SR = sustained release susp = suspension tab = tablet XL/XR= extended release Module V: Calculations of Oral Medications Math and Dosage Calculations Module Level 1_rev _pjc Page 23

24 A. Oral Solids Example: Order: furosemide 60 mg po daily Supply: furosemide 40 mg per tab. How many tablet/s will the client receive per dose? Computation: 1 tab 60 mg 60 3? tab/s = x = = = 1 ½ tablets 40 mg 1 dose 40 2 Practice Exercises: cap/s 1. The order is Tikosyn (dofetilide) 0.5 mg PO bid. Stock on hand is Tikosyn (dofetilide) 125 mcg/cap. Calculate how many capsule/s of this medication should be given to the patient. tab/s 2. The physician orders potassium chloride crystals CR 40 meq twice a day orally for a patient with hypokalemia. Potassium chloride crystals CR are available in 20 meq tablets. How many tablet/s would the nurse administer with each dose? Math and Dosage Calculations Module Level 1_rev _pjc Page 24

25 tab/s 3. Order: Increase patient's current dose of Celexa 10 mg PO daily to 20 mg per day starting next dose. See label below for dosage on hand. The new amount to administer is. tab/s 4. The physician orders acyclovir 400 mg PO three times a day for herpes. The medication is supplied in 800 mg tablets. How many tablet/s will the nurse administer? Math and Dosage Calculations Module Level 1_rev _pjc Page 25

26 B. Oral Liquids Example: The physician ordered 0.5 g of Zithromax four times daily for 3 days. What is the amount to administer? Refer to label for dosage on hand. Computation:? ml = 5 ml 200 mg x 0.5 g 1 dose x 1000 mg 1 g = 12.5 ml per dose Practice Exercises: ml 1. Order: Nilstat Oral Suspension 250,000 units PO q.i.d. Supply: Nilstat Oral Suspension 100,000 units per ml How many milliliters of the medication would be given to the patient per day? Math and Dosage Calculations Module Level 1_rev _pjc Page 26

27 Practice Exercises 2 through 4, refers to this label. ml 2. Ordered: EES Granules 400 mg PO q6h. See label above for dose on hand. The amount to administer per dose is. mg 3. How many milligrams does the whole bottle contain? (Read: Directions for mixing or reconstituting the medicine.) days 4. Based on the above computation, how many days will the whole bottle last? Math and Dosage Calculations Module Level 1_rev _pjc Page 27

28 mg 5. Ordered amoxicillin/clavulanate 875 mg every 12 hours. See label for medication on hand. What is the amount to administer? (Base dose on amount of amoxicillin available.) (Round off to the first decimal number.) Math and Dosage Calculations Module Level 1_rev _pjc Page 28

29 Module VI: Calculations of Parenteral Medications A. Injection from a Liquid Example: The physician orders furosemide 60 mg IV push stat for edema. How many milliliters will the nurse administer? Computation: 1 ml 60 mg 60? ml = x = = 6 ml per dose 10 mg 1 dose 10 Practice Exercises: ml 1. Calculate the amount to administer per day. Order: Heparin 2500 units subcutaneous injection bid Supply: Heparin units per ml Math and Dosage Calculations Module Level 1_rev _pjc Page 29

30 ml 2. Order: tobramycin sulfate 90 mg IM q8h Supply: Nebcin (tobramycin sulfate) 80 mg per 2 ml How many milliliters are you going to administer? (Round off to the first decimal number.) ml 3. Calculate the amount to administer. Choose the correctly marked syringe. syringe Ordered: Lanoxin mg deep IM stat. On hand: Lanoxin 0.25 mg/ml. Math and Dosage Calculations Module Level 1_rev _pjc Page 30

31 ml 4. The physician orders Imferon 90 mg IM (Z track) for anemia. The medication is supplied in 50 mg/ml. How many milliliters will the nurse administer? (Round off to the 1st decimal number if the dose is greater than 1 ml) ml 5.The physician orders Methergine 0.3 mg IM for postpartum bleeding. The medication is supplied in 0.2 mg/ml. How many milliliters will the nurse administer? Shade the syringe. Math and Dosage Calculations Module Level 1_rev _pjc Page 31

32 B. Injection from Powders Some medications are prepared in a dry form, powder, or crystal. As liquids, they are unstable and lose potency over time. The drug must be reconstituted according to the manufacturer s directions, which will give the type and amount of diluent to use. Example: Order: cefonicid sodium (Monocid) 0.65 g IM every day Label directions: Add 2.5 ml sterile water for injection. Shake well. Provides an approximate volume of 3.1 ml (325 mg/ml). Stable 24 hours at room temperature or 72 hours if refrigerated (5 C). Equivalent: 0.65 g = 650 mg Desire: The order is 0.65 g. Supply: The fluid portion of the solution made, it is 1 ml = 325 mg. Have: 1 g as a dry powder; when reconstituted, it is 325 mg/ml. Answer: How much liquid to give, stated as ml. Use conversion factor 1000 mg/1 g 1 ml 0.65 g 1000 mg 650 x x = = 2 ml 325 mg 1 g 325 Math and Dosage Calculations Module Level 1_rev _pjc Page 32

33 Practice Exercises: 1. Find the amount to administer. Order: Methylprednisolone 30 mg IM now. On Hand: Single dose vial. Reconstitute 1.2 ml of Bacteriostatic Water for injection. Each 1 ml (when mixed) contains: Methylprednisolone sodium succinate equivalent to 40 mg of Methylprednisolone. 2. Find the amount to administer. Order: Zyprexa 7.5 mg IM now On Hand: Zyprexa Intramuscular 10 mg Follow the steps to reconstitute: Inject 2.1 ml of Sterile Water for injection into single-packaged vial for up to 10 mg dose. Dissolve contents of the vial completely, resulting solution should be clear and yellow. Each 1 ml (when mixed) contains 5 mg of Zyprexa Intramuscular for injection solution. Math and Dosage Calculations Module Level 1_rev _pjc Page 33

34 C. Insulin Injections Practice Exercises 1 and 2 refer to this scenario. Scenario: The patient has the following order: > Humulin N 20 units subcutaneous injection every morning. > Regular Insulin subcutaneous injection ac & hs per sliding scale Blood Glucose Reading Insulin Dose per Sliding Scale mg/dl = 2 units mg/dl = 4 units mg/dl = 6 units mg/dl = 8 units Greater than 350mg/dl = call MD Stock on Hand: Humulin N 100 units per ml Regular Insulin 100 units per ml units 1. The patient s blood glucose before breakfast is 240 mg/dl. How many units of insulin will the patient receive based on the sliding scale? units 2. What is the total amount of insulin the patient will receive this morning? Math and Dosage Calculations Module Level 1_rev _pjc Page 34

35 Module VII: Dosages Based on Body Weight Rule: 1. Convert the weight from pounds to kilograms (rounded to the 1st decimal number). 2. Calculate the dosage in milligram per kilogram. Multiply mg by weight in kg. 3. Compare the ordered dosage to the recommended dosage, and decide if the dosage is safe. Example: The physician orders palifermin (Kepivance) 60 mcg/kg body weight to be administered daily. The client weighs 88 lb. The medication is supplied 5 mg/ml. How many milliliters would you administer per dose? Computation: 1 ml 60 mcg 88 lb 1 mg 1 kg 5280? ml = x x x x = = 0.48 ml 5 mg 1 kg 1000mcg 2.2 lb Practice Exercises: Scenario: The following questions refers to this scenario. The physician orders oxacillin sodium 200 mg/kg body weight per day to be given in two (2) divided doses. The client weighs 66 pounds. The medication is supplied 500 mg/ml. ml 1. How many milliliters would you administer per dose? ml 2. How many milliliters would you administer per day? Math and Dosage Calculations Module Level 1_rev _pjc Page 35