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Please explain to me why I set up this problem wrong. Dimensional Analysis


The patient weighs 117 pounds. Dopamine is running at 30 mL/hr. There is 400 mg of dopamine in 500 mL of solution. How much dopamine is the patient receiving in mcg/kg/min?

this is the way the problem is set up:

1/117lbs x 2.2lbs/1kg x 400mg/500mL x 30mL/1hr x 1hr/60min x 1000mcg/1mg = 7.5 mcg/kg/min

i did NOT set up the problem this way, I flipped all the values instead.

My question is this; why was the 117 lbs placed on the bottom and not at the top of the equation. How do you know when to place the weight on the bottom? I started the problem with 500ml over 400mg and went from there. I got the answer wrong, because everything was flipped. Can somone explain to me why the above set up is correct?

SopranoKris, BSN, MSN, RN, NP

Specializes in Critical Care. Has 6 years experience.

The question is asking for mcg per kg per minute.

(1000 mcg/1 mg) x (400 mg/500 mL) x (30 mL/1 hour) x (1 hour/60 minutes) x (1 patient/117 pounds) x (2.2 lbs/1 kg)

If you cancel out all your units, you end up with mcg/kg/min (mcg per kg per minute)

Any time you have a fraction with 3 units. The first unit is on top (numerator) and the 2nd & 3rd unit are on the bottom (denominator).



kg min

Does that make sense?

the way that problem was set up is really confusing. Just do your conversion one step at a time. Remember the unit you want should be on the top all the time

I always start out with the weight conversion .. just my preference but you don't have to.

117 lbs * 1 kg/2.2 lbs = 53.18 kg (put this answer aside, we'll use it later on)

Main problem:

30 ml/hr * 400 mg/500ml = 24 mg/hr (ml cancels out)

at this point you can do two things.. you can convert your answer mg/hr to mcg/hr or into mg/min. Eventually you want your answer in mcg/min.

24 mg/hr * 1000 mcg/mg = 24,000 mcg/hr (mg cancels out)

24,000 mcg/hr * 1 min/60 mins(hr) = 400 mcg/min (hr cancels out)

** since you want your answer in mcg/kg/min, you'd want to divide 400 mcg/min by 53.18 kg to get the dose PER KG (The value 400 mcg/min does not factor in the weight of the the patient; you need to include the weight in order to give the pt the correct therapeutic dose)

400 mcg/min divided by 53.18 kg = 7.5 mcg/kg/min (compare the 400 mcg/min vs 7.5 mcg/kg/min. Notice that w/o the weight factor in, the patient will get an excessive amount of dopamine)

Hope this helps.

I'm with Kris --

I always start out by looking at how the answer needs to be.. mcg/kg/min.. so I would start out by looking for mcg as well

thus the 1st step would be 1000 mcg/1 mg -- then just keep canceling out until you get rid of all the factors you don't need.

Edited by 203bravo

Bedside_Life RN

Specializes in Surgical Intensive Care. Has 3 years experience.

Okay, so how I begin this process is finding out the proportion of drug to total volume. So 400 divided by 500, leaves a ratio of 0.8mg per 1mL of solution. Since you have to know the ratio in mics, you simply move the decimal over to equal 800mcg per 1mL of solution. At this point make sure that the 400mg/500mL is equivalent to 400,000mcg/500mL. Wouldn't you agree this is the same?

Now, taking into consideration that there are 800mcg per 1mL, just multiply it by thirty. You should get 24,000mcg per 30mL of solution. This is the amount your patient is getting per HOUR.

So at this point you need to find out the dosage (24,000mcg per hour) divided by every Kg of your patient. If your patient weighs 117 pounds, convert pounds to kilograms, to get 53.1818182 Kg. At this point, you will have to look at your institution's rounding rules. If you round to the nearest whole number you would get 53Kg.

So how many micrograms is your patient getting per 1Kg? To find this answer divide 24,000mcg by 53Kg. You will get 452.830189mcg per 1Kg. Once again according to your institution there may be rounding rules. So lets stick with rounding to the closest whole number, 453.

At this point we know that your patient will be receiving 453mcg per 1Kg every HOUR.

Finally, you will need to take your dosage (453mcg for every 1kg) per hour and divide this by 60 minutes. So 453mcg divided by 60 minutes, gives you 7.55mcg/1kg/minute.

I know that this was a lengthy explanation but sometimes it helps to have a step by step instruction on dosage calculation. Remember, there is always more than one way to skin a cat, and as long as you get the right answer, and the right dose for your patient, you are administering a SAFE dose.

Hope this helps. Good luck!

SopranoKris! that absolutely makes sense. THANK YOU!!!!! :yes: :up:

Everyone else who took the time to answer... Thank you!! :)

SopranoKris, BSN, MSN, RN, NP

Specializes in Critical Care. Has 6 years experience.

SopranoKris! that absolutely makes sense. THANK YOU!!!!! :yes: :up:

Great! I'm glad that helped :D

What helps me the most in med math is to skip to the question and find out what I need. In this scenario it was mcg/kg/min. This tells me to look for mcg first, since I want it on the top of my equation. Since the question only gave mg, I had to start with 1000 mcg/1 mg so the mcg is in the appropriate place. From there you can plug in what eliminates mg, then eliminates mL, etc.

By starting with what you need on top first, you know your conversion ratios will always be in the right order. It also helps to weed out extraneous information they put in the question to throw you off :)