Hi. This is Cathy with Level Up RN. In this video, I will be working through a pediatric dosage calculation problem that involves weight-based dosing. So within the pediatric population, this is the most common method for determining the appropriate dose for a child. So I will first do a review on how to convert a child's weight from pounds and ounces to kilograms. And then I will work through a weight-based dosage calculation problem on my whiteboard using three different methods including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations, and our workbook will help you do just that. In a nutshell, our workbook contains all different types of dosage calculation problems that you are likely to encounter in nursing school. And we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
In this video, we are going to review how to convert a child's weight from pounds to kilograms or pounds and ounces to kilograms. And with the pediatric population, we typically need to round to at least the nearest hundredth when it comes to their weight. So let's look at these two examples. For the first example, if we have a child that weighs 71 pounds, what is their weight in kilograms? Round to the nearest hundredth. So we would just take 71 pounds and divide by 2.2, or if you prefer dimensional analysis, that's what I prefer to do, then you just multiply by this conversion factor. You definitely have to remember that there are 2.2 pounds in a kilogram. So if you calculate this out, you end up with 32.272727 and on and on and on. So we need to round to the nearest hundredth, so that'll be 32.27 kilograms. All right. Let's look at our second problem here. If a newborn weighs 7 pounds, 6 ounces, what is the weight in kilograms? And we need to round to the nearest hundredth. So when we're dealing with a weight that is in pounds and ounces, we need to first convert those ounces to pounds. So 6 ounces, 1 pound equals 16 ounces. So if I do this calculation, I end up with 0.375 pounds. So 6 ounces equals 0.375 pounds. So let's add these pounds into the 7 pounds, so we have 7.375 pounds. And now we can convert this to kilograms. So we're going to multiply this times our conversion factor, and our pounds will cross off. And when we do this math, we end up with 3.3522 and it goes on and on. But we need to round to the nearest hundredth, so this is 3.35 kilograms. And that's the answer to the second problem.
So in this problem, we have an order for amoxicillin PO 30 milligrams per kilogram per day to be administered in equally divided doses every 8 hours. So that's three times in a 24-hour period. The patient weighs 56 pounds, and amoxicillin that is available is 125 milligrams in 5 mls. And we need to make sure we round all our answers to the nearest tenth. And we're being asked four different questions. Question A is, how many milligrams will the patient receive per day? B is, how many milligrams the patient will receive per dose? And then for C, we're being asked how many milliliters the patient will receive per day? And then D, how many milliliters per dose? Okay. So let's go ahead and tackle the A part of this problem. So this is asking us how many milligrams will the patient receive per day? And our order is for 30 milligrams per kilogram per day. So right out of the gate, we know we need to convert our patient's weight from pounds to kilograms in order to determine the dose per day. So we can solve part A using dimensional analysis or ratio and proportion. I'm going to first do it with dimensional analysis because it's just a little quicker and more efficient. So here we have a weight of 56 pounds. And then I can multiply times the conversion factor to get this to kilograms. So one kilogram equals 2.2 pounds, my pounds cross off. And then I can just multiply times the ordered dose, which is 30 milligrams per kilogram per day, and we're looking for per day. So my kilograms will cross off. And if I multiply this out, I end up with 763.6 milligrams. And again, this is per day. And this number is rounded. It's rounded to the nearest tenth, which is what we were asked to do here in the problem.
You could also do the same math using ratio and proportion. If I was going to use this method, I would first convert my weight to kilograms. So I would take that 56 pounds, and I would divide by 2.2 to get the kilograms, and that is 25.45 kilograms. This four five is repeating, so if you put this number in your calculator, you'll end up with 25.45454545 and on and on, so that's what this little repeating symbol is here. Then I can set up my ratios, right? So my ratio on one side is going to be 30 milligrams per kilogram. That's my ordered dose. That's our known ratio. And we want to know how many milligrams we should give for a weight of 25.45 kilograms, okay? And then I would cross multiply here. So 1 times X is just X. And on this side, we get 30 times 25.45. And if we do that math, we end up with the same number we did over here, so 763.6 milligrams. And again, that's rounded, and that's the dose per day. So that answers A. A is going to be 763.6 milligrams per day.
B asks us, how many milligrams will the patient receive per dose? So like I mentioned when we read through this order, we're giving the patient the medication every eight hours. This is the dose per day. We're going to be giving it three times a day. So we're going to take that daily dose, divide by three, because we're giving it three times a day, and we're going to end up with 254.5 milligrams per dose. And that is rounded to the nearest tenth, which we were instructed to do here. Okay. So that's the answer to B. Now, let's go on to step C. C asks us, how many milliliters will the patient receive per day? So I'm going to erase some of my math here. I'm actually going to leave the milligrams per day because we're going to need that number. All right. So we can solve part C using dimensional analysis, ratio and proportion, or the formula method. So let's first use dimensional analysis. So if we take our daily dose, which we just figured out, 263.6 milligrams, and we multiply times the available concentration of this medication, which is 5 mls with 125 milligrams, and we set it up so that our milliliters is on top, our milligrams is on bottom, our milligrams will cross off. And if we do this math, we will end up with milliliters for the day. So if I do that math, I end up with 30.5 milliliters. So that's the answer to C; how many milliliters will the patient receive per day?
We can do the same calculation using ratio and proportion. So if I want to solve part C using ratio and proportion, I would set up my known ratio on one side of the equation, so that's 125 milligrams in 5 ml. And on the side of the equation, I would put my daily dose, which we calculated previously. And we want to find out how many milliliters that will be for the day. So now I would cross multiply, so that would be 125X equals 5 times 763.6. And then if we do this math, we end up with 3,818 divided by 125, so X would be equal to 30.5 mls, just like we got here with dimensional analysis. Few more steps involved, but you would get to the same number. And then finally, we could also do this math with the formula method as well. So our desired dose is 763.6 milligrams. And then the dose we have is 125 milligrams, and our vehicle is 5 ml. So remember with formula method, desired over half times vehicle. And if we do this math again, we end up with 30.5 ml. So the answer to C is that the patient will receive 30.5 mls per day. And this number is rounded to the nearest tenth. Okay. And then part D is how many milliliters will the patient receive per dose? Again, this patient is getting this medication three times a day. So if we take the daily amount of 30.5 mls divide by 3, we end up with 10.2 milliliters per dose. And that is also rounded to the nearest tenth. So that will be the answer to D.
