# Metric System Calculations

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1 Metric System Calculations Many of the calculations needed in nursing practice relate to the metric system. Below are two simple ways to remember some of the key calculations GRAMS MILLIGRAMS MICROGRAMS For converting grams to milligrams to micrograms follow these simple rules 1. Determine which amount is larger (Gram is larger than milligram is larger than microgram 2. The difference between each amount is a factor of or 3 decimal places. 3. So moving the decimal to the right or the left (3 spaces) will give you the correct answer 3 grams = 3000 milligram = 3,000,000 micrograms 5 micrograms = milligrams = grams (Remember there is decimal point after the 5.) KILOGRAMS TO POUNDS Most people know that the factor for converting pounds to kilogram is 2.2. But sometimes it is confusing as to whether you multiply or divide. Remember, the number of pounds is always a greater number than the weight in kilograms. So look carefully at your calculation and see if the conversion makes sense. 1 kilogram is 2.2 pounds WHAT IS THE QUESTIION ASKING? Read the question carefully to determine if the question is providing you with information for the DAILY dose, but asking you to calculate the amount given every 4, 6, or 8 hours. The following material was created by Kaiser to help prepare you for the Medication Math Test. We strongly encourage you to review the entire packet and take advantage of the practice calculations before taking the calculation test.

2 Kaiser Permanente NCAL Medication Math Toolkit Math Review & Practice Questions

3 Medication Math Toolkit Table of Contents Introduction... 3 Math Review & Practice Questions... 4 Common Conversions... 4 Calculating Dosages... 5 Calculating IV Flow Rates... 7 Calculating a Drip Rate using an IV tubing Drip Factor... 8 Calculating Units per hour... 9 Math Review Practice Questions Medication Math Resources Bibliography Page 2 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

4 Introduction According to the Institute of Medicine of the National Academies, Medication errors are among the most common medical errors, harming at least 1.5 million people every year. The impact on the health of patients as well as the staff involved in such errors is significant both financially and emotionally. This medication math review and assessment focuses on one aspect of safe medication administration--right dose. Determining the right dose frequently requires the nurse to calculate how much of the drug to give based on physician order and the medication available. It is estimated that 42% of medication errors are due to errors in administration, one step of which is drug dose calculation. The enclosed materials are intended to provide the opportunity to review the principles of drug dose calculation, provide the opportunity to practice drug dose calculations, and complete an assessment of your ability to perform this skill. It is important to continually reinforce and practice the skills necessary for accurate drug dose calculation. Page 3 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

5 Common Conversions Math Review & Practice Questions 1 gm = 1000 mg To convert grams (gm) to milligrams (mg), move decimal point 3 places to right or multiply grams (gm) by mg = gm To convert milligrams (mg) to grams (gm), move decimal point 3 places to the left or divide milligrams (mg) by mg = 1000 mcg To convert milligrams (mg) to micrograms (mcg), move decimal point 3 places to right or multiply milligrams (mg) by mcg = mg To convert micrograms (mcg) to milligrams (mg), move decimal point 3 places to the left or divide micrograms (mcg) by kg = 2.2 lb To convert kilograms (kg) to pounds (lb), multiply kg by 2.2 To convert pounds (lb) to kilograms (kg), divide lb by tsp = 5 or To convert teaspoon (tsp) to milliliters (), multiply tsp by 5 ½ tsp = gr = 60 mg ½ gr = 30 mg To convert grains (gr) to milligrams (mg) multiply by 60 To convert mg to grains (gr) divide grains by 60 Notes: This table will be provided during the test. Trailing zeroes are for illustration purposes only and should NOT be used in clinical practice. Page 4 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

6 Calculating Drug Dosage Ratio and Proportion A ratio is composed of two numbers that are related to each other. In health care, medications are often expressed as a ratio. For example: 125 mg per 1 tablet read as 125 mg/1 tablet. 250 mg per 10 read as 250 mg/10. A proportion shows two ratios that are equal, like this: 4 12 = 1 3 Calculating Dosages METHOD #1: Basic Ratio & Proportion Calculation When the dose on hand is not the same as the desired per ordered dose, the ratios can be expressed as a proportion: Dose on hand Quantity on hand = Desired dose (Drug order) Quantity desired (X) For Example: 500 mg is ordered. It is available in 250 mg capsule(s). Solve for X to get the number of capsule(s) to give. 1. Set up the proportion between the ratios: Dose on hand (250 mg) Desired dose (500 mg) = Quantity on hand (1 capsule) Quantity desired (X capsule(s)) Units of measure in the numerator must be the same on both sides of the equation. Units of measure in the denominator must be the same on both sides of the equation. 2. Cross multiply the ratios: multiply the numerator of one ratio by the denominator of the other ratio and do the same for the other two values 250 mg 1 capsule = resulting in an equation: 500 mg X capsule(s) 250 mg x X capsule(s) = 1 capsule x 500 mg Page 5 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

7 3. Solve for X (quantity desired) by dividing the multiplier of X into the right side of the equation 1 capsule x 500 mg = 500 = 2 X capsule(s) = X capsule(s) 250 mg 250 capsule(s) METHOD #2: Calculation of medication in solution For example: 5000 units are ordered. It is available in a vial containing 10,000 units/. Solve for X to get the number of to give. 1. Set up the ratio between the proportions: 10,000 Units 1 = 5000 Units X 2. Cross multiply the proportions: multiply the numerator of one ratio by the denominator of the other ratio and do the same for the other two values 10,000 Units 1 resulting in an equation: = 5000 Units X 10,000 Units x X = 1 x 5000 Units 3. Solve for X (quantity desired) by dividing the multiplier of X into the right side of the equation 1 x 5000 Units = 5000 X = 10,000 Units X = ,000 METHOD #3: Another method of calculating medication in solution Volume to be administered = Dose ordered Available concentration in 1 For example: 8 mg is ordered. It is available as 10 mg/. Volume to be administered = Dose ordered (8 mg) Available concentration in 1 (10 mg/) = 8 10 = 0.8 *** If concentration is not available for 1, you must calculate the concentration for 1 by taking the total dose and dividing it by the total volume to calculate dose per. For example: If you have 30 mg of a drug in 100, the calculation would be 30 divide by 100 = 0.3 mg/ Page 6 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

8 Calculating IV Flow Rates To find the flow rate stated in per hour (if not given in the order), solve forx which is the number of to infuse per hour For example: 1000 IV solution ordered to infuse over 8 hours 1. Set up the ratio between the proportions: 1000 = X 8 hr 1 hr 2. Cross multiply the proportions: multiply the numerator of one ratio by the denominator of the other ratio and do the same for the other two values 1000 = X 8 hr 1 hr resulting in an equation: 8 hr x X = 1000 x 1 hr 3. Solve for X (quantity desired) by dividing the multiplier of X into the right side of the equation X = 1000 x 1 hr 8 hr X = 125 /hr Page 7 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

9 Calculating a Drip Rate using an IV tubing Drip Factor The Drip Rate is the number of drops (gtts) per min to be infused (gtts/min). The Drip Factor of the IV tubing is determined by the manufacturer. This information can be found on the IV tubing packaging. The Drip Factor is the number of drops that equal 1 of solution. Example of a Drip Factor: A Drip Factor of 15 gtts/ means it will take 15 gtts of the IV solution to deliver 1 of the IV solution. To Calculate an IV Drip Rate: IV drip rate (gtts/min) = Volume to be infused (ml) x Drip Factor of tubing gtts/ time (in min) to be infused For example: 1000 of D5W ordered to be administered over 8 hours The IV tubing drip factor is 10 gtts/. 1. Convert hours to minutes. The IV infusion is ordered to be administered over 8 hours There are 60 minutes in 1 hour 8 hours x 60 minutes = 480 minutes 2. Set up the calculation to determine gtts/min using the following information: Volume to be infused is: 1000 The Drip factor is: 10 gtts/ Time is: 480 minutes The IV drip rate (gtts/min) = 1000 x 10 gtts/ 480 min The IV drip rate = gtts 480 min gtts 480 min = gtts/min Rounded to nearest whole number = 21 gtts/min Page 8 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

10 Calculating Units per hour For example: Patient is receiving 1000 units in 10 at 100 /hr. How many units is the patient receiving per hour. 1. Write a fraction to describe the known solution strength (units of drug divided by milliliters of solution): 1000 units Set up the second fraction with the flow rate in the denominator and the unknown dose in the numerator: X units Write these fractions into a proportion: 1000 units = X units Solve for x by cross multiplying: 10 x X units = 1000 units x Divide each side of the equation by 10 and cancel units that appear in both the numerator and denominator: 10 x X units = 100 x 1000 units X = 100,000 units 10 X = 10,000 units With a flow rate of 100 per hour. The patient is receiving 10,000 units per hour. Page 9 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

11 Math Review Practice Questions Below is a set of sample test questions for you to practice. During the proctored test: You will have 60 minutes to complete 20 questions. You may use the calculator, conversion table, and scratch paper provided. Personal cell phones, PDAs (Blackberries, iphones), or any other electronic devices will not be allowed. You will be expected to show your calculations for each question on the test and write your answer on the line provided. Minimum passing score is 90%. Relax and take a deep breath. 1. Convert 99 lb to kg 2. Convert 4 mg to mcg kg 3. Convert 2 gm to mg mcg mg 4. Convert 300 mg to gm gm 5. Convert 2500 mcg to mg mg 6. Ordered: 40 units Available: 100 units/ 7. Ordered: mg Available: 0.25 mg/tablet How many tablet(s) should the nurse give? tablet(s) Page 10 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

12 Math Review Practice Questions cont. 8. Ordered: 0.5 mg Available: 2 mg/ 9. Ordered: 0.3 gm Available: 300 mg/tablet How many tablet(s) should the nurse give? tablet(s) 10. Ordered: 0.03 gm Available: 6 mg/8 11. Ordered: 80 mg Available: 100 mg/ 12. Ordered: 250 mg Available: The bottle says add 9.5 of sterile water to the vial to yield 0.5 gm/ 13. Ordered: 100,000 units Available: 250,000 units/ Page 11 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

13 Math Review Practice Questions cont. 14. Ordered: 75 mg Available: 50 mg/ 15. Ordered: 70 meq Available: 200 meq/ Ordered: 0.6 mg Available: 250 mcg/ 17. Ordered: 20 mg/kg for a patient who weighs 36 lb Available: 100 mg/ 18. If your patient took 1 tsp of liquid every 15 minutes for 3 hours, how much total liquid was consumed in? 19. Ordered: 25 every 2 hours. How many will be given in 8 hours? 20. Ordered: 4 mg/kg for patient who weighs 55 kg Available: 90 mg in 10 Page 12 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

14 Math Review Practice Questions cont. * LVNs who are NOT IV certified should stop here. All other nurses may want to practice #21 through # Ordered: 120 to be infused over 30 minutes. At what rate (/hr) should the nurse set the infusion pump? /hr 22. Ordered: IV solution to run at 100 /hr. The IV tubing has a drip factor of 15 gtts/. How many gtts/min will need to be delivered? gtts/min 23. Ordered: 1000 D5W with 0.45% N/S in 6 hours How fast should the nurse run the IV in gtts/min if they are using tubing that delivers 15 gtts/? gtts/min 24. Ordered 20,000 units in 1000 to run at 30 /hour. How many units per hour is the patient receiving? units/hr Page 13 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

15 1. Convert 99 lb to kg Math Review Practice Questions (Answer Key) 99 lbs 2.2 = 2. Convert 4 mg to mcg 4 mg x 1000 = 3. Convert 2 gm to mg 2 gm x 1000 = 4. Convert 300 mg to gm 300 gm 1000 = 5. Convert 2500 mcg to mg 2500 mcg 1000 = 45 kg 4000 mcg 2000 mg 0.3 gm 2.5 mg 6. Ordered: 40 units Available: 100 units/ 100 units = 40 units 1 X 100 units x X = 40 units x 1 X = 40 units x units 0.4 Page 14 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

16 Math Review Practice Questions (Answer Key) cont. 7. Ordered: mg Available: 0.25 mg/tablet How many tablet(s) should the nurse give? 0.25 mg = mg 1 tablet X tablet(s) 0.25 mg x X tablet(s) = 1 tablet x mg X tablet(s) = 1 tablet x mg 0.25 mg 8. Ordered: 0.5 mg Available: 2 mg/ 2 mg = 0.5 mg 1 X 2 mg x X = 1 x 0.5 mg X = 1 x 0.5 mg 2 mg 9. Ordered: 0.3 gm Available: 300 mg/tablet How many tablet(s) should the nurse give? 0.3 gm x 1000 = 300 mg 300 mg = 300 mg 1 tablet X tablet(s) 300 mg x X tablet(s) = 1 tablet x 300 mg X tablet(s) = 1 tablet x 300 mg 300 mg 0.5_ tablet(s) _ tablet(s) Page 15 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

17 Math Review Practice Questions (Answer Key) cont. 10. Ordered: 0.03 gm Available: 6 mg/ gm x 1000 = 30 mg 6 mg = 30 mg 8 X 6 mg x X = 8 x 30 mg 6 mg = 8 x 30 mg 6 mg 40_ 11. Ordered: 80 mg Available: 100 mg/ 100 mg = 80 mg 1 X 100 mg x X = 1 x 80 mg X = 1 x 80 mg 100 mg _0.8 Page 16 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

18 Math Review Practice Questions (Answer Key) cont. 12. Ordered: 250 mg Available: The bottle says add 9.5 of sterile water to the vial to yield 0.5 gm/ 0.5 gm = 500 mg 500 mg = 250 mg 1 X 500 mg x X = 1 x 250 mg X = 1 x 250 mg 500 mg 13. Ordered: 100,000 units Available: 250,000 units/ 250,000 units = 100,000 units 1 X 250,000 units x X = 1 x 100,000 units _ 0.5 X = 1 x 100,000 units 250,000 units Ordered: 75 mg Available: 50 mg/ 50 mg = 75 mg 1 X 50 mg x X = 1 x 75 mg X = 1 x 75 mg 50 mg 1.5 Page 17 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

19 Math Review Practice Questions (Answer Key) cont. 15. Ordered: 70 meq Available: 200 meq/ meq = 70 meq 10 X 200 meq x X = 10 x 70 meq X = 10 x 70 meq 200 meq Ordered: 0.6 mg Available: 250 mcg/ 0.6 mg x 1000 = 600 mcg 250 mcg = 600 mcg 1 X 250 mcg x X = 1 x 600 mcg X = 1 x 600 mcg 250 mcg Ordered: 20 mg/kg for a patient who weighs 36 lb Available: 100 mg/ 36 lb 2.2 = kg (rounded down to 16 kg or rounded up to 16.4 kg) 20 mg x kg = mg 100 mg = mg 1 X 100 mg x X = 1 x mg X = 1 x mg 100 mg Page 18 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

20 3.27 (Rounds to 3.3 ) Math Review Practice Questions (Answer Key) cont. 18. If your patient took 1 tsp of liquid every 15 minutes for 3 hours, how much total liquid was consumed in? 1 tsp x 5 = 5 3 hours x 60 = 180 min 5 = X 15 min 180 min 15 min x X = 5 x 180 min X = 5 x 180 min 15 min Ordered: 25 every 2 hours. How many will be given in 8 hours? 25 = X 2 hrs 8 hrs 2 hrs x X = 25 x 8 hrs X = 25 x 8 hrs 2 hrs 20. Ordered: 4 mg/kg for patient who weighs 55 kg Available: 90 mg in 10 4 mg x 55 kg = 220 mg 90 mg = 220 mg 10 X 90 mg x X = 10 x 220 mg 100 X = 10 x 220 mg 90 mg _ (Rounds to 24.4 ) Page 19 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

21 Math Review Practice Questions (Answer Key) cont. * LVNs who are NOT IV certified should stop here. All other nurses may want to practice #21 through # Ordered: 120 to be infused over 30 minutes. At what rate (/hr) should the nurse set the infusion pump? 30 min 60 = 0.5 hr 120 = X 0.5 hr 1 hr 0.5 hr x X = 120 x 1 hr X = 120 x 1 hr 0.5 hr 240 /hr 22. Ordered: IV solution to run at 100 /hr. The IV tubing has a drip factor of 15 gtts/. How many gtts/min will need to be delivered? 1 hour x 60 = 60 mins X = Volume to be infused x Drip Factor of tubing time (in min) to be infused X gtts/min = 100 x 15 gtts/ 60 min 25 gtts/min 23. Ordered: 1000 D5W with 0.45% N/S in 6 hours How fast should the nurse run the IV in gtts/min if they are using tubing that delivers 15 gtts/? 6 hours x 60 =360 min X = Volume to be infused x Drip Factor of tubing time (in min) to be infused X gtts/min = 1000 x 15 gtts/ Page 20 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

22 360 min 41.6 gtts/min (Rounds to 42 gtts/min) Math Review Practice Questions (Answer Key) cont. 24. Ordered 20,000 units in 1000 to run at 30 /hour. How many units per hour is the patient receiving? 20,000 units = X units x X units = 20,000 units x 30 X units = 20,000 units x X units = 600,000 units units/hr Page 21 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

23 Medication Math Resources Chocked full of basic to more advanced math review questions and answers: 1. Schilling, J. (2009). Dosage Calculations an Incredibly Easy Workout. Lippincott, Williams & Wilkins. Philadelphia. 2. A web site with basic medication calculation concepts Take practice quizzes on equivalencies, abbreviations, basic ratio & proportion, IV infusion rates, OB dosage and IV quizzes, pediatric quizzes, and titration for critical care nurses A web link to register for a 45 contact hour extensive review course in medical math. Cost is \$ and the learner may take up to 4 months to complete the course A self study module on Fundamentals of Mathematics for Nursing Luz Martinez de Castillo, S., Werner-McCullough, M. (2007). Student Workbook to Accompany Calculating Drug Dosages: An Interactive Approach to Learning Nursing Math, 2 nd Ed. F.A. Davis, Philadelphia. Includes a CD with modules on a variety of medication review topics from basics to titration of IV s with quizzes. 7. Website with nursing medication calculators Practice with everyday math including fractions, decimals and ratio and proportion Page 22 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

24 Bibliography 1. Baiyasi, S., Constan, Dewey, E. (2001) Math for Nursing and Allied Health. Delta College: Teaching & Learning Center. Retrieved July 22, 2008 from: d%20allied%20health.pdf 2. California Community Colleges: Regional Health Occupations Resource Center (2004). Strategies for Student Success in Health Occupations: A Model Curriculum. Chancellor s Office of California Community Colleges. 3. McAlister, C., Shapiro, S. (2006). Fundamentals of Mathematics for Nursing. Retrieved July 22, 2008 from: 4. Schilling, J. (2009). Dosage Calculations an Incredibly Easy Workout, Lippincott, Williams & Wilkins. Philadelphia. 5. Schilling, J. (2005). Dosage Calculations Made Incredibly Easy, 3 rd Ed. Lippincott, Williams & Wilkins. Philadelphia. Page 23 of 23 (Adapted from FINAL Version 4.0, 1/9/09)

25 Common Conversions 1 gm = 1000 mg To convert grams (gm) to milligrams (mg), move decimal point 3 places to right or multiply grams (gm) by mg = gm To convert milligrams (mg) to grams (gm), move decimal point 3 places to the left or divide milligrams (mg) by mg = 1000 mcg To convert milligrams (mg) to micrograms (mcg), move decimal point 3 places to right or multiply milligrams (mg) by mcg = mg To convert micrograms (mcg) to milligrams (mg), move decimal point 3 places to the left or divide micrograms (mcg) by kg = 2.2 lb To convert kilograms (kg) to pounds (lb), multiply kg by 2.2 To convert pounds (lb) to kilograms (kg), divide lb by tsp = 5 or To convert teaspoon (tsp) to milliliters (), multiply tsp by 5 ½ tsp = gr = 60 mg ½ gr = 30 mg To convert grains (gr) to milligrams (mg) multiply by 60 To convert mg to grains (gr) divide grains by 60 Notes: Trailing zeroes are for illustration purposes only and should NOT be used in clinical practice. Page 1 of 1 (Adapted from FINAL Version 4.0, 1/9/09)

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