DOSAGE PRACTICE PROBLEM

GUIDE

SOUTHERN UNIVERSITY SCHOOL OF NURSING

NURSING 410/415

Revised Fall 2010

Developed by: Latricia Greggs, Fall, 2007

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Practice Problem Guide

This practice problem guide focuses on learning additional drug calculations

necessary for nursing practice. Students have already learned basic calculation methods

to safely compute oral dosages, conversion between metric, apothecary and household

measurements, parenteral dosages, and intravenous flow rates. Students will expand their

knowledge of calculating intravenous medications along with dosages based on body

weight with time. Also students will learn to add medications to IV fluids and consider

the total fluid volume infused after the mediation is added. More complicated IV

problems including titration, and adjusting fluids will be explained.

RATIONALE:

The implications involved in the administration of medications should be taken

seriously by all professional nurses. The nurse has a legal, moral, ethical, and

professional responsibility to ensure that clients receive the right dosage of a medication,

and practice drug administration in a safe and effective manner. Nurses must be able to

compute medication doses accurately, efficiently, and measure medications correctly. A

careless mistake can lead to a fatal error.

EXPECTED OUTCOME:

1. Convert within and between selected measurement systems: Metric, Household, & Apothecary.

2. Calculate dosages for administration of medications by common routes: Oral medications – tablets, oral liquid volumes, and parenteral medication.

3. Calculate infusion rates and times for intravenous administration: volumes between ml/hr, gtts/min; total and end infusion times of IV fluids; amounts and times to administer IV push medications; infusion rates and times for intermittent infusions (piggyback).

4. Calculate dosages of individual clients given the client’s weight.

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5. Calculate titrated IV flow rates and dosages based on weight and time; units per hour (units/hr), micrograms per kilogram per minute (mcg/kg/min), micrograms per minute (mcg/min), milligrams per minute (mg/min)

6. Demonstrate knowledge of adding medications to IV fluids and determining the correct flow rate based on the 5 % rule

7. Demonstrate ability to reconstitute single and multiple strength doses.

ACTIVITES:

Students may utilize the Practice Problem Guide, text, and sources from previous

level nursing courses, OB/Peds, N304, and N210. An opportunity will be given for

students to meet with their Nursing 410/415 faculty. Additional calculation books may

be obtained from the library. There are also on-line resources available.

Special Note: Many of you have learned D X Q to work dosage problems. It would learn ADimensional Analysis especially when it comes to working equivalents (conversions).

Dimensional Analysis

Dimensional Analysis (DA) is becoming a popular method for dosage calculation because it involves simple multiplication and division. The advantage of using DA is that only one equation is needed even if the information given requires you to convert to like units.The following are steps for Dimensional Analysis

Step 1: On the left side of the equation, place the name or abbreviation of the drug form of x, or what you are solving for

x capsules =

Step 2: On the right side of the equation, place the available information related to the measurement or abbreviation that was placed on the left side. This information is placed as a common fraction, matching the appropriate measurement.

x capsules = 1 capsule (numerator) 250 mg (denominator)

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Step 3: Find the information that matches the measurement or abbreviation used in the denominator of the fraction you created. In this example mg is in the denominator and the order is for 500 mg

x capsules = 1 capsule x 500 mg 250 mg 1

Identify appropriate equivalent with a 1:1 ratio (e.g. 1 g = 1000 mg). Set up the equation so that labels can be canceled; for example mg is in the numerator, mg must be in the denominator to cancel.

Step 4: Now cancel out the like abbreviations or the right side of the equation. If you have set up the problem correctly, the remaining measurement should match that used on the left side of the equation. You are now ready to solve for xSolve the equationa. Cancel labels first; the answer label should not cancelb. Reduce numbers to lowest termsc. Multiply/divide to solve equation.d. Reduce answer to lowest terms, convert to decimal, and round to a measurable quantity.

x capsules = 1 capsule x 500 mg = 500 = 2 capsules 250 mg 1 250

Dosages ordered as mg/kg/day or mg/kg

Step 1 Find client’s weight in kilograms. Convert pounds (lbs) to kilogramsConversion 1 kg = 2.2lbsRound kgs nearest one hundredth (follow hospital P & P)

Weight in lbs = wt in kgs 2.2 (lbs/kg)

Ordered: Drug X 1 gm Q 4 hours by mouthPatient weighs 195 lbsThe recommended dose is 40 – 50 mg/kg/dayIs the ordered dose safe?Step 1: 195 lbs ÷ 2.2 = 88.64 kgs

Step 2: 40 mg/88.64kgs = 40 x 88.64 = 3545 mg

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50 mg/88.64ks = 50 x 88.64 = 4432 mg

Dose to be given Q 4 hours meaning 24 ÷ 4 = 6 doses

1 gm = 1000mg x 6 doses = 6000 mgNo – the dose ordered is not within a safe range

Flow Rates (IV) (Review)

Flow rate is the amount of medication to be infused over a certain time period. Flow rate is ordered by the physician; however the nurse must set and maintain the rate.Electronic pumpManual IVs

Calculating using “drop factor” found on each manufacture’s IV tubing (manual IV)

Based as drops per minute (gtt/min)Drop factor is the number of drops per ml of liquid that an IV tubing set will drop into its drip chamberStandard manufactures drop factors areMacro Micro10 gtt/ml 60 gtt/ml15 gtt/ml20 gtt/ml

ExamplesOrdered: 250 ml Lactated Ringers (LR) to infuse @ 50 ml/hrDrop Factor 20 gtts/ ml

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Ordered: Pantoprazole (Protonix) 40 mg in 100 ml sodium chloride 0.9% IVPB to infuse over 30 minsDrop factor = 10

Infusion rate in ml/Hr _______200 ml/hr___________Infusion rate in gtts/min_______33 gtt/min_________

Calculating Powdered medications (Reconstitution of meds)

Usually the pharmacist reconstitutes and mixes drugs. Because some drugs are not stable in liquid form, on occasions you will have to reconstitute at the time of administration. Use only the solvent designed on the label or manufacturer insert to ensure compatibility.

5 % Rule

NOTE: The application of the 5% rule ensures accuracy of the flow rate of IV fluids.

When adding medications to IV fluids, the total amount of solution needs to be considered when determining flow rate. The greater the solution that is added, the more important it is to include this amount in computation of flow rate of solution. Refer to the health care agency policy regarding application of the 5% rule

5% Rulea. If the volume of the drug to be added is equal to or greater than 5 % of the

amount of IV fluid to be administered, the two solutions should be added together. The IV flow rate should be calculated on the amount of IV fluid PLUS the volume of medication.

b. If the volume of the drug to be added is less than 5% of the total amount ordered to be administered, the amount is usually considered negligible and is not necessary to add the two solutions together

Adding drugs to IV’s, calculating gtt/min and ml/hr (amt less than 5% total)

Aminophylline 750 mg in 1000 ml D5W is ordered at 20 mg/hr. Pharmacy supplies the Aminophylline in vials of 500 mg/20 ml

How much aminophylline is to be added to the 1000 ml?Calculate gtt/min using DF = 15Calculate the flow rate for the pump

Adding drugs to IV’s, calculating gtt/min and ml/hr ( amt greater than 5% total)

A stat order states that aminophylline 400 mg in 50 ml of D5W IVPB is to be given over 60 minutes. The drug is available 500 mg/25 ml.

How many ml of aminophylline would you add to the IV bag?

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What is the total amount of solution in ml?What is the drop rate/min if the DF = 15?Calculate the flow rate for the pump?

Medications by units/HourHeparin dripsInsulin drips

There are special meds that are very potent and need to be monitored closely. It is crucial to maintain accuracy in the calculation of these drug dosages and IV flow rates. It can mean the difference of life or death for your patient. All of these medications must be administered by IV electronic pump (ml/hr) for safe administration.

You have a patient who has deep vein thrombosis and has orders for heparin at 1000 units/hr. The concentration of heparin sent from pharmacy is heparin 25,000 units in 500 ml 0.9% NS. How many ml/hr should the IV pump be programmed for? ____20 ml/hr____

DA

ml/hr = 500ml x 1000 units = 500,000 = 20 ml 25,000 units 1 Hr 25,000

You have an order for your patient with diabetes to receive regular insulin IV at 12 units/hr. The concentration is insulin 100 units in 250 ml of 0.9% NS. How many ml/hr should the IV pump be programmed for __30 ml/hr_____

DA

ml/hr = 250 ml x 12 units = 3000 = 30 ml/hr 100 units 1 hr 100

Using the formulas above you will also be able to determine units per hour the client is receiving.

Units/hr = 100 units x 30ml = 3000 = 12 units/hr 250 ml 1 hr 250

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Titrated Orders

Critically ill patients in a hospital often receive special medications that are very

potent and need to be monitored closely. Some drugs used in the critical care setting

may be ordered to be infused by amount of drug per kilogram of body weight per minute.

Theses are called titrations. They are based on the manufacturers provided

recommended dosage and the patient’s body weight measured in kilograms. It is

extremely important to accurately monitor the flow of these medications; therefore most

are delivered by IV machine. Because of the serious nature of these drugs, route of

administration and state of the patient it cannot be overemphasized how important the

accuracy of the calculation of the drug dosage and IV flow rates is. It is a matter of life

and death. (Ogden, S. J., Calculation of Drug Dosages Seventh Edition, Mosby, 2003, pg

341). They are used in life threatening situations to alter or maintain vital physiologic

functions, for example heart rate, cardiac output, blood pressure, respirations and renal

function. These drugs in general have a rapid action and short duration. They may be

administered by IV push or bolus, but also diluted in 250-500 ml or IV solution, most

commonly D5W. (Curren, A. M., Munday L. D., Dimensional Analysis for Meds, WI

Publications, Inc. 1998, pg 246). Titration refers o the adjustment of dosage within a

specific range to obtain a measurable physiologic response, for example Levophed 2-4

mcg/min to maintain systolic BP greater than 100. The dosage is increased or decreased

within the ordered range until the desired response is obtained. (pg. 255)

Examples of these titrations are mg per minute, mcg per minute, or units

per hour. Dimensional analysis can be used to calculate flow rate, or when the flow rate

is the dosage being administered per unit of time. Other methods include learning

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formulas. The dosage may be titrated according to the patient’s weight each day. In that

case, the dose per minute or hour must be multiplied by the patient’s weight in kg, then

perform the calculations.

IV administration of medications by microgram/kilogram/minute

Example: 800 mg of dopamine is added to 250 ml of 0.9% NS. The order is to begin the infusion at 3 mcg/kg/min. The patient’s weight is 70 kg. The nurse needs to calculate how many ml/hr the IV pump should be set for.

Step 1: 3 mcg/kg/min = 3 mcg/70kg/min = 210 mcg/min

Step2: ml = 250 ml x 1 mg x 210 mcg x 60 min = 3,150,000 = 3.9375 or 3.9 ml/hr Hr 800 mg 1000mcg 1 min 1 hr 800,000IV administration of medications by microgram /minute

Example: 50 mg of nitroglycerin has been added to 500 ml 0.9% NS. The order is to infuse the nitroglycerin at 5mcg/min. The nurse needs to calculate how many ml/hr the IV pump needs to be set for.

ml = 500 ml x 1mg x 5 mcg x 60 min = 150,000 = 3 ml/hrhr 50 mg 1000mcg 1 min 1 hr 50,000

IV administration of medications by milligram/minute

Example: Lidocaine 1 gm has been added to 500 ml of D5W. The order states to infuse the lidocaine at 2 mg/min. The nurse needs to calculate how many ml/hr the pump should be set for. Also determine how many gtts/min, using a minidrip.

ml = 500 ml x 1 gm x 2mg x 60 min = 60,000 = 60 ml/hrhr 1 gm 1000mg 1 min 1 hr 1000

gtts = 60 gtts x 500 ml x 1 gm x 2 mg = 60000 = 60 gtts/minmin 1 ml 1 gm 1000mg 1 min 1000

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Dosage Rounding Rules

As a general rule, carry work to nearest hundredth during computation of dosage problem. Don’t round off until the end of the problem. For final answer round to10th unless the amount to be administered is less than one ml. If volume is less than one milliliter then it should be rounded to hundredth.

Remember to focus on what he problem is asking for to determine the final rounding.

For example:

When the problem asks you to solve for amount of milligrams to be given, final answer should be rounded to the nearest hundredth.When the item asks you to solve for amount to administer in milliliters, tsp, etc., the final answer should be rounded to tenths.

Weight conversion: When converting lbs to kg, the student should carry to third place (thousand) and round to hundredth. (Round final answer to 100 th .) Round the final answer to tenths after computing the entire dosage problem

ORALS: Carry out to hundredth, then round final answer to nearest 10th.

Rounding correctly insures the exact amount ordered is administered. Remember that a medication can be measured using a syringe. This will be a more precise measurement than can be obtained using a medicine cup.

Parenterals: Round IV flow rate to nearest whole number – whether it is regular gtt or microgtt. Remember that microgtt means 60gtt/ml

IV Pumps: There are some IV Pumps manufactured that allow the nurse to set rate in tenths. Therefore, when computing dosage problem related to rate by pump, the student may state whole number or round appropriately to tenths.

Practice Problems:

1. Ordered: Aquamephyton 0.01g IM Q dayAvailable: Aquamephyton 10 mg per ml in 2.5 ml vialAdminister ___________ ml.

2. Ordered: promethazine HCL (Phenergan) 25 mg POAvailable: 4 oz bottle of promethazine HCL which contains 6.25 mg/5 ml.How many teaspoons (tsp) should be administered.

3. Ordered Heparin sodium 8,000 units SC Q 8 hoursAvailable: 10 ml vial containing10, 000 units/ml

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How many ml should be administered?

4. Ordered: Benadryl 30 mg PO TID PRN for c/o rash & itching to abdomen Available: Benadryl 14 ounce (oz) bottle containing 12.5 mg/5 ml.How many ml will the nurse administer?

5. Ordered Nitroglycerin 1/150 gr SL prn for chest pain. Take no more than 2 tablets in 15 min. The patient took 2 tablets. How many mg did he receive?

6. Ordered: Penicillin G 200,000 units IM Q 6 hrsAvailable: Penicillin G 250,000 units/mlGive ________________ml

7. Ordered Novolin N (NPH) insulin U-100 32 units and Novolin R insulin U-100 4 units ac breakfast daily.Give _______________units total

8. Order: Infuse 1 pack (350 ml) of packed red blood cells over 3 hoursDrop factor is 10gtt/mlFlow rate: _____________ ml/hr.

9. Ordered: Heparin 25,000 units IV in 250 ml D5W to infuse at 6 ml per hour. How many units per hour is the patient receiving?

10. Ordered 200 units regular insulin in 250 ml NS to infuse at 7 units per hour IvHow many ml per hour is the patient receiving?

11. Ordered ciprofloxacin (Cipro) 400 mg /D5W 200 ml IVPB BID. To be infused over 60 minutes.Drop factor is 15 gtt/ml

_____________ml/hr_____________ gtt/min

12. The physician orders 1000 ml D5W to infuse at 125 ml per hr. The IV administration tubing shows a drop factor of 15 gtt per ml. How many gtt per minute will the nurse administer?______________ gtt/min

13. The physician orders 0.5 mg per kg aminophylline (Phyllocontin) q6h. The client weighs 98 lbs. How many mg will the nurse administer per day?

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14. The physician orders 1.5 million units streptokinase (Streptase) IV. Available is Streptase 600,000 units powder for reconstitution. Directions state to add 4.7 ml Ns for a concentration of 600,000 units in 5 ml solution. How many ml will the nurse administer?

15. Ordered: D51/2NS to infuse over 13 hoursDrop factor = 20 gtt/ml_______________ ml/hr_______________ gtt/min

16. Mr. M is receiving heparin continuous infusion at 12 units/kg/hr. Available: premix heparin 25,000 units in 500 ml. Mr. M’s weight is 90 kg.

What rate will the nurse set on the infusion pump to the nearest ml (whole number)?

How many units per hour of heparin should the patient receive?

17. Your patient with a thoracotomy receives penicillin G 1.2 million units IM in s single dose today. The label states to dilute with 11.5 ml of diluent to yield a concentration of 1,000,000 units/ml. How many ml will the nurse administer? (1.2 ml)

18. Your patient with osteomyelitis receives penicillin G 600,000 units IM bid. Available is Penicillin G 1, 000,000 units/ml. How many ml will the nurse administer? (0.6 ml)

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Conversion Chart

METRIC APOTHECARY HOUSEHOLD1 GM (g) = 1000mg = 15 GRAINS (gr)

60 mg = 1 GRAIN (GR) * Accurate1 kilogram (kg) 2.2 pounds (lbs)

1 lb = 16 oz.1 minim ( m or min) = 1 drop (gtt)

1 cc = 1 ml = 15 or 16 minims (m )30 cc or ml = 8 drams (dr ) = 1 ounce (oz ) = 2 Tablespoons (T)

4 cc = 1 dram (dr )5 cc = 1 teaspoon (tsp.)

3 tsp. = 1 T1000 micrograms (mcg) = 1 mg

30 ml 1 fluid ounce (fl oz)240 ml 8 fl oz 1 medium glass

1000 milliliters (ml) = l liter (L) 1 quart or 32 fl oz

Note: U 100 means 100 Units of Insulin = 1cc

** Note that 60 mg = one grain is preferred when calculating medications

IV PUMPS: There are some IV Pumps manufactured that allow the nurse to set state in tenths. Therefore, when computing dosage problem related to rate by pump, the student may state whole number or round appropriately to tenths.

CONVERSION TO WEIGHT FROM LBS. TO KG.: When converting lbs to kg, the student should carry to third place (thousand) and round to hundredth. The student should round the final answer to tenths after computing the entire dosage problem

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Titration Practice Problems

1. Ordered Drug X IV infusion 200 mcg/min. Available Drug X 250 mg/1000 ml D5W. What will the flow rate be in ml/hr?

2. Levophed is ordered at the rate of 3 mcg/min. The solution strength is 8 mg Levophed in 250 ml D5W. Calculate the ml/hr flow rate.

3. A 10 mcg/min dosage of Levophed is ordered using an 8 mg/250 ml D5w solution. Calculate the gtt/min for a microdrip.

4. A 250 ml D5w solution with 1 mg Isuprel is to be infused at 5 mcg/min. Calculate he gtt/min flow rate for a microdrip.

5. Esmolol 2.5 g in 250 ml D5W has been ordered at a rate of 100 mcg/kg/min for a patient weighing 230 lbs. Calculate the flow rate on the IV pump.

6. Dobutrex 5 mcg/kg/min has been ordered using a 500 mg/250 ml D5w strength solution. The patient weights 99.4 kg. Calculate the flow rate.

7. A continuous infusion of Isuprel is ordered for a newly admitted client in cardiogenic shock. The solution strength is 2 mg in 500 ml D5W, and the rate of infusion is 40 ml/hr. Calculate the mcg/min infusing.

8. A solution of 5 g Breviblock in 500 ml D5W is infusing at 30 ml/hr. Calculate the mcg/min infusing.

9. Levophed 2-4 mcg/min has been ordered to maintain systolic BP greater than 100 mm/Hg. The solution being titrated has 8 mg Levophed in 250 ml D5W. Calculate the flow rate for the 2-4 mcg range. Calculate the lower 2 mcg/min flow rate first.

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Practice Problem Guide Key

1. 1 ml2. 4 tsp3. 0.8 ml4. 12 ml5. 0.8 mg6. 0.8 ml7. 36 units8. 116 ml/hr9. 600 units/hr10. 8.8 or 9 ml/hr11. 200 ml/hr

50 gtts/min 12. 31 gtts/min 13. 89 mg 14. 12.5 ml 15. 77 ml/hr, 26 gtt/min 16. 21.6 or 22 mL/hr, 1080 or 1100 units/hr 17. 1.2 mL 18. 0.6 mL

Titration Practice Problem Key

1. 48 ml/hr2. 5.6 ml/hr or 6 ml/hr3. 18.8 or 19 ml/hr4. 75 gtt/min5. 63 ml/hr6. 14.9 or 15 ml/hr7. 2.7 mcg/ min8. 5000 mcg/min9. A dosage of 2-4 mcg/min is delivered by a flow rate of 3.8 or 4 – 7.5 or 8 ml/hr

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