Dosage Practice Problem Guide

DOSAGE PRACTICE PROBLEM GUIDE

SOUTHERN UNIVERSITY SCHOOL OF NURSING NURISNG 304 SPRING 2007

Developed by: Latricia Greggs, 2007

1

Special Note: Many of you have learned D X Q to work dosage problems. It would A be wise to also learn ratio-proportion especially when it comes to working equivalents (conversions) and even better if you learn dimensional analysis (DA). Just keep in mind you may have to work dosage problems in steps. Oral Dosages Examples Ordered: Digoxin 0.25 mg PO each day Available: Digoxin 0.125 mg per tablet How many tablets will the nurse administer? Ratio & Proportion 0.125 : 1 tablet : : 0.25 mg : X 0.125 X = 0.25 mg 0.125 0.125 X = 2 tabs Formula

D X Q A

0.25 mg X 1 = 2 tabs 0.125 mg Dimensional Analysis (DA)

Ordered: Potassium Chloride (KCL) 60 mEq BID Available: KCL 40 mEq per 30 ml How many ml will the nurse administer?

Ratio & Proportion 40 mEq : 30 ml : : 60 mEq : X ml 40 X = 1800 40 40

2

X = 45 ml

Formula D X Q A

60 mEq X 30 = 1800 40 mEq 40

=

45 ml

DA

Equivalents – Apothecary & Metric & Household Two different measures used to calculate meds dosages Apothecary & Metric system. Currently majority of hospitals & MDs use metric, but still some physicians use apothecary (grains, kg). As nurses you must be able to use both systems. KNOW EQUIVALENTS, CONVERSIONS By definition Equivalent – a given quantity which is considered to be of equal value to a quantity that is expressed in a different system Be able to convert from one system to another (refer to conversion table, and learn conversions) Examples Ordered: Phenobarbital grain (gr) ¾ PO BID Available: Phenobarbital elixir 20 mg per 5 ml How many ml will the nurse administer? Ratio & Proportion Step 1 60 mg : 1 gr : : X : ¾ gr 1 X = 60 X ¾ X = 60/1 X ¾ X = 15/1 X 3/1

3

X = 45 mg

Step 2 20 mg : 5 ml : : 45 mg: X 20 X = 225 20 20 X = 11.25 ml Formula D X Q A

45 mg X 5 = 2.25mg X 5 = 11.25ml 20 mg

DA

Meds ProcessPub for calculating dosages Step 1: What do you have? Step 2: What do you need? Step 3: Do you need to convert from one measure system to another? Step 4a: If yes, FIRST find equivalent measurement by converting “need’ to “have” then set up an equation with what you know about basic equivalents. Step 4b: If no, set up an equation with what you know about basic equivalents Step 5: Solve for X if required Ordered: Tagamet 0.6 gm Available: Tagamet 300 mg per tablet How many tablets will the nurse administer? Follow steps Step 1 What do you have?

4

300 mg per tablet Step 2 What do you need? 0.6 gm Step 3 Do you need to convert? Yes gm ≠ mg Step 4a First find equivalent measurement by converting “need” to “have” 1gm = 1000mg so 0.6 gm = 600 mg 1000 mg : 1 gm : : X : 0.6 gm 1X = 600 X = 600 mg Step 4b then set up equation with what you know about basic equivalents Ratio & Proportion 300 mg : 1 tab : : 600 mg : x 300 x = 600 300 300 X = 2 tabs D xQ A

600 x 1 + 2 tabs 300

DA

5

The physician orders 500 mg erythromycin base (E-mycin) PO TID. Available is erythromycin suspension 200 mg per 5 ml. How many teaspoons should the client be instructed to take for each dose? Ration & Proportion Step 1 200 mg : 5 ml : : 500 mg : x ml 200 x = 2500 200 200 X = 12.5 ml Step 2

5 ml : 1 tsp : : 12.5 ml : x 5 x = 12.5 5 5 X = 2.5 tsp

D X Q A

500 x 5 ml = 2.5 x 5 = 12.5 ml ÷ 5 ml = 2.5 tsp 200

DA

Ordered: Mylanta 30 ml by mouth PC QID Available: 12 ounce (oz) bottle of Mylanta There are _________ doses in one 12 oz bottle? How many ounces will the nurse administer per dose? Ration & Proportion Equivalent - 30 ml =1 ounce 30 ml x 12 = 360 ml ÷ 30 = 12 There are 12 doses in a 12 oz bottle

6

30 ml : 1 oz : : 30 ml : x 30 x = 30 30 30 x = 1 oz Parenteral Dosages Examples Ordered: Atropine gr 1/200 Available: Atropine 0.4 mg per ml (0.4 mg/ml) How many ml will the nurse administer? Ratio & Proportion Step 1 Conversion gr ≠ mg 60 mg : 1 gr : : x : 1/200 gr 1x = 60/200 x = 0.3 mg

60 mg = x (cross multiply) 1 gr 1/200 gr 1x = 60/200 x = 0.3 mg

Step 2 Solve for ml 0.4 mg : 1 ml : : 0.3 mg : x 0.4x = 0.3 mg 0.4 0.4 X = 0.75 ml

0.4 mg = 0.3 mg (cross multiply) 1 ml x 0.3 = 0.4 x 0.4 0.4 0.75 ml = x

D x Q A 0.3 mg x 1 0.4 mg

= 0.75 ml

DA

7

Ordered: Demerol 30 mg IM every 4 hours PRN pain Available: Demerol 25 mg per 0.5 ml How many ml will you administer? Ration & Proportion 25 mg : 0.5 ml : : 30 mg : x

25 mg = 30mg 0.5 ml x 25 x = 15 25 25 x = 0.6 ml

25 x = 15 25 25 X = 0.6 ml D x Q A 30 x 0.5 ml = 1.2 x 0.5 = 0.6 ml 25 DA

The physician orders 250 mg cefazolin (Kefzol) IVPB Q 8 hours. Available is Kefzol 0.5 g per 10 ml. How many ml will the nurse administer? Ratio & Proportion 1000 mg : 1 g : : 250 mg : x

1000mg = 250 mg (cross multiply) 1g xg 1000 x = 250 1000 1000 x = 0.25 g

1000 x = 250 1000 1000 X = 0.25 g 0.5g : 10 ml : : 0.25g : x

0.5 g = 0.25 g 10 ml x 0.5 x = 2.5 0.5 0.5 x = 5 ml

0.5 x = 2.5 0.5 0.5 X = 5 ml D x Q A

0.25 g x 10 = 0.5 x 10 = 5 ml 0.5 g

8

DA

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. The physician orders 25 mg chlordiazepoxide hydrochloride (Librium) IM Q 6 h PRN. The package’s insert states: “Add 15 ml Normal Saline Solution (NSS) to yield a concentration of 100 mg per 2 ml.” How many ml will you administer? Meds Pub Follow these steps Step 1 What do you have? 100 mg per 2 ml Step 2 What do you need? 25 mg Step 3 Do you need to convert? No ( mg = mg) Solve for x ml Ration & Proportion 100 mg : 2 ml : : 25 mg : x 100 x = 50 100 100 X = 0.5 ml Q 6 hrs

D xQ A

100 mg = 25 mg 2 ml x 50 = 100 x 100 100 0.5 ml = x

25 mg x 2 ml = 0.25 x 2 = 0.5 ml 100 mg

9

DA

The physician orders 500 mg ticarcillin sodium (TICAR) IM Q 8 hours. The package insert states: “Add 8.7 ml (D5W) to yield a concentration of 1 g per 3 ml ( lg/3 ml). How many ml will you administer? What do you have? 1 g per 3 ml What do you need? 500 mg Do you need to convert? Yes g ≠ mg First find equivalent measurement by converting need to have You know that 1000 mg = 1g so 500 mg = 0.5 g Solve for x ml Ratio & Proportion 1 g : 3 ml : : 0.5 g : x ml 1 x = 1.5 x = 1.5 ml Q 8 hrs

D x Q A

1 g = 0.5 g 3 ml x ml 1 x = 1.5 1 1 X = 1.5 ml Q 8 hrs

0.5 g x 3 ml = 0.5 x 3 = 1.5 ml Q 8 hrs 1g

DA

10

Dosages ordered as mg/kg/day or mg/kg Step 1 Find client’s weight in kilograms. Convert pounds (lbs) to kilograms Conversion 1 kg = 2.2lbs Round 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 mouth Patient weighs 195 lbs The recommended dose is 40 – 50 mg/kg/day Is 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 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 mg No – the dose ordered is not within a safe range Insulin Administration Standard unit of measure for insulin is the unit. Most insulin is dispensed in “U-100”. This means that there are 100 units of insulin in 1 ml of liquid. Most insulin is dispensed in bottles containing 10 ml of liquid. You must draw up insulin in a U-100 insulin syringe.

Example The physician orders 25 units isophane insulin suspension NPH (Humulin N) and 23 units regular insulin (Humulin R) S Q in AM. You have 100 units per ml available. How many total units will the nurse administer? 23 units (clear) + 25 units (cloudy) = 48 units insulin for am dose

11

The physician orders 20 units of isophane insulin (Novolin N) 100 units/ml AC Dinner SC @ 1630 and the following sliding scale insulin (Novolin R) 100 units/ml AC and HS SC. At 1630 your client’s blood sugar is 249. How many total units of insulin will the nurse administer? Sliding Scale BS=140-169 give 3 units, BS=170-199 give 4 units, BS=200-249 give 6 units, Bs=250299 give 8 units, BS greater than 300 give 10 units. 6 units (Novolin R) + 20 units (Novolin N) = 26 units for 1630 dose Flow Rates (IV) 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 pump Manual IVs Formulas You may use the formulas taught in pharmacology or use the following: Flow rate (rate of pump) = Total volume ordered ( milliliters ) Total time in hours Calculation of Infusion Time Infusion time = Volume to be infused (ml) Flow rate Meds Pub (same as flow rate formula) Process for calculating flow Rate for electronic IV pumps Step 1: What are the total ml? (convert if necessary) Step 2: What are the total hours? Step 3: Divide total ml by total hours to find ml/hr Round to nearest whole number Examples Ordered: 1000ml D51/2NS to infuse in 8 hours. The drop factor is 15. How many ml/hr will you infuse? 1000 ml = 125 ml/hr 8 hrs

12

A provider orders 1 gram of Vancomycin in 250 ml of D5W to infuse over 90 minutes for a patient with Urinary Tract Infection. The nurse is running the IV piggyback on the infusion pump. What infusion rate should be set on the pump? 250 ml x 60 = 15000 = 166.6 or 167 ml/hr 90 mins 90 OR 90 ÷ 60 = 1.5 hrs 250 = 166.6 or 167 ml/hr 1.5 hrs 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 chamber Standard manufactures drop factors are Macro Micro 10 gtt/ml 60 gtt/ml 15 gtt/ml 20 gtt/ml

Formulas for manual IVs drops/minute Gtts/min = Total volume to be infused (ml) x drop factor (df) Total amount of time in minutes Pharmacology formula (You must remember when using this formula the time may not always be 60 mins. It may be 30 min, 20 min, or 15 min. Gtts/min = df x cc/hr 60 (time in mins)

13

Meds Pub (Simple formula) Drop factor has a standard “drop factor constant” that you can use to calculate flow rates of manual IVs This is obtained by dividing 60 by the drop factor Drop factors DF Constant 60 = 6 Simple formula 10 gtts/ml Total ml/hr = flow rate (gtt/min) Drop factor constant 60 = 4 15 gtt/ml 60 20 gtt/ml

=3

60 =1 60 gtt/ml Examples Ordered: 250 ml Lactated Ringers (LR) to infuse @ 50 ml/hr Drop Factor 20 gtts/ ml Drop factor constant is 3 (60÷20) What is the flow rate in gtt/min? Formulas 50 ml x 20 = 0.83 x 20 = 16.6 or 17 gtt/min 60 20 x 50 =0.33 x 50 = 16.6 or 17gtt/min 60 50 3

= 16.6 or 17 gtt/min (constant)

Ordered: Pantoprazole (Protonix) 40 mg in 100 ml sodium chloride 0.9% IVPB to infuse over 30 mins Drop factor = 10 Infusion rate in ml/Hr _______200 ml/hr___________ Infusion rate in gtts/min_______33 gtt/min_________ 100 ml = 200 ml/hr 0.5 hrs 200ml x 10 = 3.33 x 10 = 33.3 or 33 gtt/min 60 min OR

14

100 ml x 10 = 3.33 x 10 = 33.3 or 33 gtt/min 30 10 x 200 = 0.166 x 200 = 33.3 or 33 gtt/min 60 OR 10 x 100 = 0.33 x 100 = 33.3 or 33 gtt/min 30 200 = 33.3 or 33 gtt/min 6

(constant)

Medications by units/Hour Heparin drips Insulin 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____ Using the ratio – proportion method (Formula set-up) 25,000 unit : 500 ml :: 1000units : x ml 25000 x = 500,000 X = 500,000 25000 X = 20 ml/hr 25000 units = 1000 units (cross multiply) 500 ml x ml

15

D x Q method A Formula set-up

1000 units x 500 ml (cancel out) 25,000 units 1000 units x 1 50 units 1000 = 20 ml/hr 50

DA

You have an order for your patient with diabetes to receive regular insulin! V 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_____ Ratio – Proportion Method 100 units : 250 ml : : 12 units : x ml 100 x = 3000 x = 3000 100 X = 30 ml/hr D x Q Method A 12 units x 250 ml 100 units 12 x 2.5 = 30 ml/hr

16

DA

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

17

Chart METRIC 1 GM (g) = 1000mg = 60 mg = 1 kilogram (kg) 1 cc = 1 ml = 30 cc or ml = 4 cc = 5 cc = 1000 micrograms (mcg) = 1 mg 30 ml 240 ml 1000 milliliters (ml) = l liter (L)

APOTHECARY 15 GRAINS (gr) 1 GRAIN (GR) * Accurate 2.2 pounds (lbs) 1 lb = 16 oz. 1 minim ( m or min) = 15 or 16 minims (m ) 8 drams (dr ) = 1 ounce (oz ) = 1 dram (dr )

HOUSEHOLD

1 drop (gtt) 2 Tablespoons (T) 1 teaspoon (tsp.) 3 tsp. = 1 T

1 fluid ounce (fl oz) 8 fl oz 1 quart or 32 fl oz

1 medium glass

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

18

Practice Problems: 1. Ordered: Aquamephyton 0.01g IM Q day Available: Aquamephyton 10 mg per ml in 2.5 ml vial Administer ___________ ml. 2. Ordered: promethazine HCL (Phenergan) 25 mg PO Available: 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 hours Available: 10 ml vial containing 10,000 units/ml 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 hrs Available: Penicillin G 250,000 units/ml Give ________________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 hours Drop factor is 10gtt/ml Flow 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 Iv How 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

19

_____________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? 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 hours Drop factor = 20 gtt/ml _______________ ml/hr _______________ gtt/min Key

20