 Hello and thank you for watching Nursing School Explained. Today I'll be going over dimensional analysis to solve math problems. As you all know, dosage calculation quizzes are very common either just by on themselves or on exams. And I find the principle of dimensional analysis to be very helpful in order to figure out any math problem no matter how complicated it gets. So today what I'll do is I'll break down the different steps of dimensional analysis, the basic principle behind it, and then we'll go do some examples together so that you know how to apply this information. So the basic principle of dimensional analysis is to cross cancel. And I've written down several examples over here. So 1 divided by 1, we can cross this out, equals 1. 237 divided by 237, we can cross this out, equals 1. 3593 divided by 3593 crosses out, equals 1. Now we can do the same with units of measure. Milliliters divided by milliliters, equals 1. Kilograms by kilograms, 1. And hour divided by hour, equals 1. So this is the basic principle for dimensional analysis. When we get to our math problems, we'll be setting these up in different dimensions, so in different fractions, and we'll be looking to see where we can cross cancel things so that we always end up with 1 and the units can't turn out. And then all we have to do is do the remaining math. Now those of you that are familiar with the metric system might know this already, but I've written down very important things to memorize over here for your conversions. So these are basically ratios that you'll just have to memorize. Most of you will know these, but I've just written them down here for a nice reminder. So first of all, I always like to abbreviate pounds with the pound sign rather than writing L, B, S. Because if I have, let's say 17 pounds, I might interpret this L as a one, and then all of a sudden I have 171, and my math will be off. So I prefer to write down the pound sign for pounds, and then on the 2.2 pounds equals 1 kilo. 1000 microgram equals 1 milligram, 1000 milligrams equals one gram, 1000 grams equals one kilogram, and 60 minutes equals one hour. So I've written down several examples. Bear with me, the first few are very simple that you could probably even figure out in your head, but I just really want to get to the very basic principles of dimensional analysis and see how it's applied in even very simple examples. And then from there we can take it and move it to more complicated or more in-depth math problems. So first example here, we have an order for primal 640 milligrams, and we have available 20 milligram tablets. And the question is how many tabs are we going to administer? So we always start by writing out what we are looking for, tabs and then equals. So then we look into our math problem, what we have given, so we have 20 milligrams, and this really should be per tab. So then because really these tabs could be tabs over one, so I want the tabs to be on top. So we have tab by 20 milligram, and then we have our 40 milligram supply here. And really this again could be put over one. So now what I can do by this principle here of cross-canceling, I could cross-cancel the milligrams here, which equals one. I'm left with tabs, which is what I'm looking for here, and then I simply do my math. So 40 divided by 20 is two tabs. That would be my answer. Example number two, I have an order for Tylenol, 150 milligrams. My supply is 100 milligrams per 5 mL. Most likely this is a pediatric example. How many milliliters am I going to administer for the patient? So now I'm looking for milliliters, so I'll write this out here, milliliters equals. Now I look in my numbers that I have given, where is my milliliters? So the milliliters are on the top. So because the milliliters, I want to be left with those in the end, I'm going to write those all in the top. So 5 mL per 100 milligrams. And what my order is is 150 milligrams. And again I could put this over one. So then I can cross-cancel by the same principle, milligrams and milligrams. What I've left is, is the milliliters, which is what I was looking for here. Then I simply do my math. And this comes out to be 7.5 milliliters. Example number three, now we have an order for normal saline to be administered at 75 milliliters per hour. Our drop factor for our IV-2 bin is 15 drops per minute. So now the question is how many drops per minute will I administer? And drops is, the abbreviation is GTT. So now we're looking for drops per minute. So GTT per minute. And please always write this in the fraction with an numerator and a denominator on the top and bottom. And again this is what I'm looking for, so I equal. Now I look in here as to what do I have given that has drops. So right here I have my drops. So 15 GTT per minute, this should be milliliter, sorry everybody, per milliliter. So I have 15 drops per milliliter. And then I'll see what I have given here. I have the 775 milliliters per hour. So in order to apply my principle of cross-cancelling here, I need to have the milliliters once on the bottom and then the next time on the top. Because what I do want in the end is drops per minute. So now I write my milliliters on the top. So I'll write my next fraction here. 75 milliliters per hour. Now the milliliters I can cancel here. I need drops per minute, but I have drops per hour. This is not what I'm looking for. So now I need to convert the hours into minutes. And we know 60 minutes equals one hour. So now because I want to get rid of the hour, eventually I need to write the hour on the top and the 60 minutes on the bottom. I cancel out the hour and I'm left with minutes on the bottom, drops on the top, which is exactly what I'm looking for, and I do my math. And this comes out to be 18.75. Keep in mind drops. There is never a half a drop, a quarter of a drop, a 0.75 of a drop. Drops are always whole numbers. So this will round up to 19 drops per minute. Now this brings up a good point about rounding rules. Your school might have a particular set of rounding rules that they follow. For typically for milliliters per hour, it is rounded to the one decimal place. Drops are always rounded to the whole number. And if there was something, a result that would come out as to less than zero, a lot of times it's rounded to two decimals. So this is the rules that I'm going to apply here, but please check with your professors and the rules of your nursing school that they apply for the actual problems that you'll be getting on an exam for dosage calculations, because of course that can be altering the result and making going from correct to incorrect. So then we have another example over here. We have heparin 1,400 units per hour, that's our order. Our supply is 25,000 units for 250 ml. So that's 25,000 units in a 250 ml bag. And we want to know how many milliliters per hour are we going to administer for this patient to give the patient the 1,400 units per hour. So again, I start with what I'm looking for. Milliliters per hour. Now I start looking at what match is here. I like to first look at the numerator here. So milliliters I have given here in my ratio 250 by 25,000. So I need to have the 250 on the top because that's where I need my milliliters to be. So 250 ml by 25,000 units. And this is another thing I like to do is write out units, because if you get to write quickly and you write 25,000 units, eventually you might be sloppy and then all of a sudden becomes 250,000. And you don't know what unit that is anymore. So if you have a very sloppy writing, the U, if you just use U for units, that could be interpreted as a zero or a U. So be very careful as to how you do this and just come up with your own method. But I personally like to write out the units. Therefore, I know that it's not a zero and I don't mistake it for a zero. So I have my 250 ml by my 25,000 units. And so now I need the hour here on the bottom and I need to get rid of these units. So the other fraction that I have given here are the 1400 units per hour. I know I need the units on the top so I can cancel these out and the hour on the bottom because that's what I want to be left with. So I'm going to write 1400 units. Again, the units cross cancel. What I'm left with is the milliliters per hour, which is what I'm looking over here. And then this comes out to 14 milliliters per hour. The important point here also is look at your result and see if it makes sense. If it comes out to be something like a crazy number, 979 milliliters per hour. That's a very fast rate for heparin to be infusing. Just kind of double check and see does it make sense to be infusing heparin that fast. Also, if I administered this at 900 some milliliters per hour, I'm going to be going through two bags per hour. Actually almost four bags per hour because my bag is 250 ml. Any kind of high-risk medication, particularly heparin, they won't be coming in a very big volume because there's so much room for error if it's miscalculated or administered at the wrong rate. So look at your result and see does it make sense. Same if it comes out the result is to 0.00897 whatever. 0.0 typically doesn't make sense, especially if you're talking about maybe a small volume that you would administer to a pediatric patient over here. If you work in the NICU for example, 0.1 digit or two digits might be okay, but 0.0 typically how you're going to measure this and dry it up in a syringe. So always think about does your result make sense as to the medication that you're giving and the volume in how that could apply to patient care.