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**Dimensional Analysis Math Guide**

Diana Blum MSN

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In any drug calculation problem, for exam purposes, if you do not include the proper unit in your answer; it will be WRONG! If you do not show your work in dosage calculation on the Exams, your answers will be considered wrong !

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***Remember You may have to perform several conversions before you can obtain the answer you are seeking ***

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**For oral things like tablets, capsules, etc. Remember DO/DA**

Dose ordered x desired med (cap, tab, ml) = amount to be given Dose Available Weight Based Problems When mg/kg/day is ordered, this is not a division problem, it is a multiplication problem Intravenous fluid must be set for a given rate It must be measured as ml/hour, L/hour or drops/min. To control or adjust the flow rate only drops per minute are used.

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**The formula for working out flow rates is:**

Volume (mL) x drop factor gtt (drips)= Rate (gtt/min) (MUST be whole number) Time (min) mL (Volume)

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**Steps Determine what you want to know.**

Read the problem What is it asking? Determine what information you already know. Setup the problem using only what you need to know. Pick a starting point pick from what you know and make sure you put it in the right place Or pick a factor that is given, such as what the physician ordered. • Be aware that the starting factor will always have at least one unit that is not desired. This will need to be changed using a cancellation technique Keep trying to cancel out units you don't want until you end up with only the ones you do If you can't get to what you want: try picking a different starting factor Did you Convert everything?

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It is time to Solve It: Make sure all the units other than the answer units cancel out, then you are ready to do the math. a. Simplify the numbers through cancellation. Same number on top and bottom: these should cancel out b. Multiply all the top numbers together, then divide into that number all the bottom numbers.. Don’t Put the decimal in the wrong spot. Don’t add incorrectly always double check. d. Round off the calculated answer if possible. e. Add labels to the appropriately rounded number to get your answer. Always work the problem backwards to check accuracy.

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**Pumps like to be programmed in mL/hr, so mL/hr are your answer units. **

You need to start a continuous drip of amiodarone at 1 mg per minute (by pump). The standard IV mixture is 450 mg in 250 mL. Pumps like to be programmed in mL/hr, so mL/hr are your answer units. 1mg x 60min x 250ml = 33.3ml/hr 1min hr mg Milrinone Lactate (Primacor) has been ordered for a patient at 0.4 mcg/kg/min. The patient weighs 145 kg. If the pharmacy mixes 20 mg of Milrinone in 100 mL of total solution, what would be the rate of the infusion? First, think what units will be in the answer. Since you're using a pump, it's mL/hr. 145kg x 0.4mcg x 1mg x ml x 60min= 17.4ml/hr 1kg/1min mcg mg hr

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Practice Calculate the drip rate for 100 mLs of IV Fluids to be given over a half hour via a giving set which delivers 10 drops/ml. 2. Calculate the drip rate for 2 liters of IV Fluids to be given over 5 hours via a giving set which delivers 10 drops/ml.

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3. A client is ordered 20 milligrams of Haloperidol decanoate by intramuscular injection. 50 milligrams in 1 milliliter of liquid for IM Injection is available. How many milliliters will you administer? 4. A client is ordered 200 milligrams of Augmentin 600 intravenously. 600 milligrams in 6 milliliters of liquid for IV Injection is available. How many milliliters will you administer?

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**5. The IV ordered is 1000 mL to infuse at 160 mL/hour**

5. The IV ordered is 1000 mL to infuse at 160 mL/hour. Calculate the infusion time in hours and minutes for this order 6. The order is for nitroprusside 50 mg in 250 mL D5W to infuse at 3 mcg/kg/min for a patient whose weight is 75 kg. Calculate the hourly infusion rate in mL/hr.

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7. The order is for dopamine 200 mg/500 mL D5W to infuse at 10 mcg/kg/min for a patient whose weight is 75 kg. Calculate the hourly flow rate in mL/hr. 8. The physician orders dopamine (Intropin) 400 mg in 250 mg D5W TRA 5 mcg/kg/min. For the client who weighs 110 lbs, how many ml /hr will the pump be set?

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**9. Nitroglycerin is infusing at 16 ml/hr**

9. Nitroglycerin is infusing at 16 ml/hr. The bag has 50 mg NTG in 250 ml D5W. How many mcg/min is the client receiving? 10.Ms. Bellman is post-op CABGx5. She has an order of dobutamine 3 mcg/kg/min. The 250 ml bag of D5 indicates 250 mg of Dobutrex. Her weight is 130 lbs. What is the flow rate? 11. Mr. Muruski is being treated for shock. The dobutamine infusion is set at 34 ml/hr. The medication label indicates Dobutrex 250 mg in 250 ml D5. His weigh is 190 lbs. What is the dosage of dobutamine the client is receiving?

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**Answers 33gtts/min 67 gtts/min 0.4 ml = 2 ml**

ml x 1 hr = hours then .25hrs x 60min = 6 hours and 15 mins 160ml hour mcg/75kg/60min= 13500mcg/hr or 13.5mg/hr 250ml x 13.5mg = 68mL/hr 50mg hr

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**7. 10mcg/75kg/60min= 45000mcg/min or 45mg/hr**

500ml x 45mg =112.5 or 112ml/hr 200mg 1 hr / 250 = 1.6 mg/ cc = 1600 mcg/cc 2) Convert lbs to kg. 110 / 2.2 = 50 3) Dose (5) x kg (50) x 60 / concentration (1600) 5 x 50 x 60 = 15,000 15, 000 / 1600 = 9.375 9. 50 / 250 = 0.2 mg/cc = 200 mcg/cc Rate (16) x Concentration (200) = 3200 / 60 = 53.33 kg Concentration is 1000 mcg/ml. 11. Wt. = kg. Concentration = 1000 mcg/ml (34 x 1000) / (86.6 x 60)

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