DOSAGE PRACTICE PROBLEM

GUIDE

SOUTHERN UNIVERSITY SCHOOL OF NURSING

NURISNG 304

SPRING 2007

Developed by: Latricia Greggs, 2007

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Special Note: Many of you have learned D X Q to work dosage problems. It would Abe 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 DosagesExamplesOrdered: Digoxin 0.25 mg PO each dayAvailable: Digoxin 0.125 mg per tabletHow 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 tabs0.125 mg

Dimensional Analysis (DA)

Ordered: Potassium Chloride (KCL) 60 mEq BIDAvailable: KCL 40 mEq per 30 mlHow many ml will the nurse administer?

Ratio & Proportion

40 mEq : 30 ml : : 60 mEq : X ml

40 X = 1800 40 40

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X = 45 ml

Formula D X Q 60 mEq X 30 = 1800 = 45 ml A 40 mEq 40

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 definitionEquivalent – a given quantity which is considered to be of equal value to a quantity that is expressed in a different systemBe able to convert from one system to another (refer to conversion table, and learn conversions)ExamplesOrdered: Phenobarbital grain (gr) ¾ PO BIDAvailable: Phenobarbital elixir 20 mg per 5 mlHow 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

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X = 45 mg

Step 2 20 mg : 5 ml : : 45 mg: X

20 X = 225 20 20

X = 11.25 mlFormula D X Q 45 mg X 5 = 2.25mg X 5 = 11.25ml A 20 mg

DA

Meds PubProcess for calculating dosagesStep 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 gmAvailable: Tagamet 300 mg per tabletHow many tablets will the nurse administer?Follow stepsStep 1 What do you have?

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300 mg per tabletStep 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 & Proportion300 mg : 1 tab : : 600 mg : x

300 x = 600 300 300

X = 2 tabs

D x Q 600 x 1 + 2 tabsA 300

DA

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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 & ProportionStep 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 500 x 5 ml = 2.5 x 5 = 12.5 ml ÷ 5 ml = 2.5 tspA 200

DA

Ordered: Mylanta 30 ml by mouth PC QIDAvailable: 12 ounce (oz) bottle of MylantaThere 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 = 12There are 12 doses in a 12 oz bottle

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30 ml : 1 oz : : 30 ml : x 30 x = 30 30 30x = 1 oz

Parenteral DosagesExamplesOrdered: Atropine gr 1/200Available: 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 60 mg = x (cross multiply)1x = 60/200 1 gr 1/200 gr x = 0.3 mg 1x = 60/200

x = 0.3 mg

Step 2 Solve for ml

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

0.75 ml = xD x QA

0.3 mg x 1 = 0.75 ml0.4 mg

DA

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Ordered: Demerol 30 mg IM every 4 hours PRN painAvailable: Demerol 25 mg per 0.5 mlHow many ml will you administer?

Ration & Proportion 25 mg : 0.5 ml : : 30 mg : x 25 mg = 30mg

0.5 ml x25 x = 15 25 x = 15 25 25 25 25 X = 0.6 ml x = 0.6 ml

D x QA

30 x 0.5 ml = 1.2 x 0.5 = 0.6 ml25

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) 1 g x g

1000 x = 250 1000 x = 250 1000 1000 1000 1000 X = 0.25 g x = 0.25 g

0.5g : 10 ml : : 0.25g : x 0.5 g = 0.25 g10 ml x

0.5 x = 2.5 0.5 x = 2.5 0.5 0.5 0.5 0.5 X = 5 ml x = 5 ml

D x Q 0.25 g x 10 = 0.5 x 10 = 5 mlA 0.5 g

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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 PubFollow these stepsStep 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 mg = 25 mg 100 x = 50 2 ml x 100 100 X = 0.5 ml Q 6 hrs 50 = 100 x

100 100 0.5 ml = x

D x Q 25 mg x 2 ml = 0.25 x 2 = 0.5 mlA 100 mg

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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 mlWhat do you need? 500 mgDo you need to convert? Yes g ≠ mgFirst find equivalent measurement by converting need to haveYou 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 g = 0.5 g 1 x = 1.5 3 ml x ml x = 1.5 ml Q 8 hrs 1 x = 1.5

1 1 X = 1.5 ml Q 8 hrs

D x Q 0.5 g x 3 ml = 0.5 x 3 = 1.5 ml Q 8 hrsA 1 g

DA

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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

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

Insulin AdministrationStandard 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

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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 ScaleBS=140-169 give 3 units, BS=170-199 give 4 units, BS=200-249 give 6 units, Bs=250-299 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 pumpManual 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 TimeInfusion time = Volume to be infused (ml)

Flow rate

Meds Pub (same as flow rate formula)

Process for calculating flow Rate for electronic IV pumpsStep 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 numberExamplesOrdered: 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

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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 90OR 90 ÷ 60 = 1.5 hrs

250 = 166.6 or 167 ml/hr1.5 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 chamberStandard manufactures drop factors areMacro Micro10 gtt/ml 60 gtt/ml15 gtt/ml20 gtt/ml

Formulas for manual IVs drops/minuteGtts/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)

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Meds Pub (Simple formula)Drop factor has a standard “drop factor constant” that you can use to calculate flow rates of manual IVsThis is obtained by dividing 60 by the drop factorDrop factors DF Constant60 = 6 Simple formula10 gtts/ml Total ml/hr = flow rate (gtt/min)

Drop factor constant60 = 415 gtt/ml

60 = 320 gtt/ml

60 = 160 gtt/mlExamplesOrdered: 250 ml Lactated Ringers (LR) to infuse @ 50 ml/hrDrop Factor 20 gtts/ mlDrop 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/min60

50 = 16.6 or 17 gtt/min (constant) 3

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_________

100 ml = 200 ml/hr 0.5 hrs

200ml x 10 = 3.33 x 10 = 33.3 or 33 gtt/min 60 minOR

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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/min60OR10 x 100 = 0.33 x 100 = 33.3 or 33 gtt/min 30

200 = 33.3 or 33 gtt/min (constant) 6

Medications by units/HourHeparin dripsInsulin dripsThere 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

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D x Q methodAFormula 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 MethodA

12 units x 250 ml100 units

12 x 2.5 = 30 ml/hr

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DA

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

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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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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 containing 10,000 units/mlHow 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

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_____________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 hoursDrop factor = 20 gtt/ml_______________ ml/hr_______________ gtt/min

Key

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