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- I just received this drug calculation problem from a
- nursing student, and I think it's essential that the nursing
- students out there are able to do this, just in case I'm the
- patient receiving the drug.
- So let's do it.
- And I think it's an interesting unit conversion problem for
- pretty much anyone who wants practice with unit conversion.
- So the question is that we have a doctor.
- The doctor orders drug x.
- And this is the dosage that the doctor's requesting.
- They're saying five milligrams per pound of patient weight-- I'll
- just write per pound of patient weight-- every twelve hours.
- This is what we're supposed to do.
- But our supply of the drug-- it isn't just, you know, not
- just nuggets and milligrams.
- It's a solution.
- There's a certain amount of grams for every milliliter
- that we have of the solution.
- It's dissolved in some water.
- So this is our supply of drug x.
- We have 0.9-- I'll write a 0 in front.
- My wife, who is a doctor, says it's essential to write the
- zero in front of the decimal.
- We have 0.9 grams per milliliter of solution.
- So if I were to take one milliliter out of my solution
- and give it to someone, I'm essentially giving them
- 0.9 grams of this drug.
- And the final piece of information we're given is that
- the patient-- they weigh-- and maybe we should say they mass,
- because kilograms is mass, but we get the idea.
- The patient is 72.7 kilograms.
- So there's a couple interesting things here.
- We have to figure out the dosage in terms of milliliters.
- We have to-- oh, actually, I didn't even tell
- you the question.
- The question is, how many milliliters of solution
- do we have to give to the patient per dose?
- So milliliters of solution per dose.
- That's our question.
- And there's a couple of things.
- We have to go from milligrams to grams.
- And then convert that to milliliters.
- And then they tell us per pound, but then they gave us
- the patient's weight, or their mass, in kilograms.
- So we have to do some conversion there.
- So I definitely can appreciate how this can be a little
- daunting and maybe confusing at times.
- So let's just do it step by step.
- So the first interesting thing-- and this is just
- something that you might need to know, or you might have
- written down on paper, or you might have a calculator that
- does this-- is just how to convert kilograms to pounds.
- And it's good to know in general, if you're converting
- between the metric and the English systems.
- So 1 kilogram is approximately equal to 2.2 pounds.
- Not exactly, but that's a pretty good approximation.
- And one pound-- if you just take one over that-- one pound is
- approximately equal to 0.45 kilograms.
- So we'll just put this in a box.
- This is the only kind of outside conversion information
- we'll need to do this problem.
- Everything else, we'll just need a calculator, unless we
- just want to spend a lot of time doing some arithmetic.
- So the first thing.
- Let's figure out our dosage in terms of per kilogram.
- This is per pound, and we really don't need to
- know every twelve hours.
- Because they're saying, how many milliliters of solution
- do we do per dose?
- A dose is every twelve hours.
- So we just really, you know-- the every twelve hours is kind
- of extra information.
- So we want to figure out this five milligrams per pound.
- How do we convert that to how many milligrams per kilogram?
- So let's do five-- I'll write it down here in magenta--
- five milligrams per pound.
- And then we want to convert this to per kilogram.
- So we can multiply this times the number of pounds per
- kilogram-- I'll do it in yellow-- times this
- information up here.
- Times 2.2 pounds per kilogram.
- And if you ever get confused-- you know, gee, how did Sal know
- to multiply by 2.2 instead of dividing by 2.2?
- Which is the same thing as multiplying by 0.5.
- You can pay very close attention to the units.
- Notice, I wrote 2.2 pounds per kilogram.
- 2.2 pounds per 1 kilogram.
- And you know this'll work out, because you have a pound in
- the numerator and you have a pound in the denominator.
- It's called dimensional analysis.
- If you ever get confused with these things-- and I think,
- once you do enough practice, you'll find that you won't
- have to pay too much attention to this.
- But at first, when you're getting started, just to make
- sure you're not multiplying or dividing by the wrong
- thing, just make sure the dimensions cancel out.
- Pounds in the numerator, pounds in the denominator.
- So let's do that.
- Pounds in the numerator, pounds in the denominator cancel out.
- And you multiply 5 times 2.2.
- This is equal to-- let's see.
- five times two is ten.
- 5 times 0.2 is 1.
- So this is equal to eleven.
- And then in our numerator, we have milligrams.
- eleven milligrams per kilogram.
- So we just converted our dosage information to
- a pure metric system.
- It was actually a mix between the metric and the
- English system before.
- Now let's see what we can do.
- Well, let's see if we can get it in terms of how many
- milliliters we have to deliver per pound.
- So once again, we want this-- well, actually, let's
- go to grams first.
- Because we have milligrams here.
- We have grams up here.
- So let's see if we can convert this thing to grams.
- So just like we did before, we want a milligrams
- in the denominator.
- I'll do it in orange.
- We want a milligrams in the denominator and we want
- a gram in the numerator.
- Why did I say that?
- Because I want this and this to cancel.
- And I want a grams in the numerator.
- So how many grams are there per milligram?
- You can just think it through.
- There's one gram per one thousand milligrams.
- Or one thousand milligrams per gram.
- And you just multiply it out.
- So the milligrams cancels with the milligrams, and then
- we get-- this is equal to eleven / one thousand grams per kilogram.
- So now we have everything in terms of grams, but we want
- it in terms of milliliters.
- The question is, how many milliliters of
- solution per dose?
- So let me go down here on this line right here.
- So we had this result.
- We have eleven / one thousand-- I won't do the division just yet-- grams
- of drug x per kilogram.
- This is really just a re-- we've just rewritten
- this dosage information in different units.
- And let's see how much solution we need per kilogram.
- So I want to cancel out the grams here and have
- a milliliters there.
- So to cancel out that grams, I'm going to have to have a
- gram in the denominator and a milliliter in the numerator.
- So in our solution, how many grams are there per milliliter?
- Well, they told us.
- There are 0.9 grams per milliliter.
- Or for every 1 milliliter, there are 0.9 grams.
- Notice, I just took the inverse of that.
- Because we want a milliliter in the numerator, grams in
- the denominator, so that these two cancel out.
- And let's do this multiplication now.
- So our grams cancel out.
- We have milliliters per kilogram.
- And then we multiply it out.
- 11/1,000 times 1 over 0.9.
- So I'll just keep-- let me just write it like this.
- So there's going to be 11/1,000 times 0.9 milliliters of
- our solution per kilogram.
- So we've gotten this far.
- So this is per kilogram of patient body weight.
- And then finally, they tell us how many kilograms
- our patient weighs.
- So let's do that last multiplication, and then we can
- actually get our calculator out and do it all at once.
- So let's multiply this times-- we want to know how many
- milliliters per patient.
- We want the kilograms to cancel out.
- So we want kilograms per patient.
- Now we're talking about this particular patient.
- Not every patient is going to be the same
- number of kilograms.
- But if we do this, kilograms will cancel out.
- We'll have milliliters per patient-- milliliters of
- solution per patient-- which is exactly what we want.
- We want milliliters of solution per dose per patient.
- But everything we've assumed so far has been per dose.
- So how many kilograms does the patient weigh?
- Well, there's 72.7 kilograms per patient.
- That's how much the patient weighs.
- So we just do this final multiplication and
- we'll be done.
- So our answer-- and as these two things are going to cancel
- out-- so our final answer is going to be 11 times 72.7
- divided by 100 times-- actually, 100 times 0.9 is
- pretty easy to figure out.
- That's nine hundred.
- Divided by nine hundred milliliters per patient.
- Or you can just say milliliters per dose.
- However you want to say it.
- Per dose per patient.
- Let's get our calculator out and do this.
- So we have 11 times 72.7 is equal to 799 divided by 900.
- Is equal to 0.88-- well, we could round up.
- 0.889.
- Hopefully the doctor won't mind.
- So that is equal to-- I'll write it in a nice, vibrant
- color-- 0.889 milliliters of solution per dose.
- So this is what we're going to give every twelve hours.
- If they ask, how many total milliliters over the
- course of two days?
- We would have to say, oh, there's forty-eight hours.
- We'd multiply it by four.
- But that twelve hours was extra information in this problem.
- But anyway, hopefully this is useful, and it'll ensure that
- any nurses serving me in the future are giving me
- my proper dosage.
- And hopefully, the doctor even got the right dosage to begin
- with, because otherwise it's all for naught.
- Anyway.

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