Struggling with Dimensional Analysis?

All right guys. So as y'all jump in,
okay,
Jim in the comments, if you're in the chat, let me know you're here and we'll get started in like, you know, 30 seconds or so. Give people a chance to jump on. All right. [inaudible] okay. All right guys. So we are going to talk about dimensional analysis. So yeah, so dimensional analysis is a method for doing dosage calculation. Um, and in my personal opinion is the method for doing dosage calculation. Um, a lot of times you'll learn like different formulas depending on the different, um,
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types of questions that you're doing or different things that you're looking for you on a different formula every time. So then you have to remember which formula to use and what's different about it. And I just don't like that. I think it's too confusing and it leads you down too many different roads. He, Chris. So I liked dimensional analysis. The biggest benefit of dimensional analysis is that you do it the same way every single time and you end up with one calculation, not multiple. Okay. All your conversions are included in the same place. Everything is in one place. You don't have to worry about remembering different formulas are converting and when do you round one calculation. So I loved mental analysis for that reason. So what I'm gonna do is I'm going to give you the six, five steps to dimensional analysis. We're going to work a couple of problems together and then if you guys have questions or if you have other problems, don't me work out.
We will do it. Okay? So what you guys to be ready to write this down because these are your major, um, steps to dimensional analysis and you're going to do it this way every single time. Okay? So step number one, and I'm just going to go through these. You can write them down and then we will actually talk about, excuse me, I kept the hiccup seal. We'll actually talk about what they mean as we go through the practice problems. So first thing, step one is always start with what you're looking for. Start with what you're looking for and you'll see what that means when we work it out. Okay? Start with what you're looking for. Number two is transfer your units across or up, across or up. And again, you'll see what that means when we do the things. So start with what you're looking for. Transfer your units across or up.
Insert what you know or convert if you don't. So insert what you know or convert if you don't insert, known or convert. Okay? Now step four is easy. It's just repeat two and three, right? Insert what you know, convert. If you don't transfer your units across there up, insert what you know, convert. If you don't transfer your and it's across their app. So how do we know when we're done? We are going to do that and you're going to cancel your units until you get your desired results. And again, your desired result is what you're looking for, right? So cancel your units until you get your desired result. Once you get your desired result of units at the end, then you're going to multiply across the top, divide across the bottom, and do that all in one calculation. All right, so I'm gonna hold this here for just a second. Take a screenshot if you need to write it down. Have these steps in front of you as we work out our problems.
Okay. All right, so let's work out a couple of problems. The beauty of of dimensional analysis again is that you can do at the same way for every type of problems, we're going to go from really simple to more complicated. Okay. And then if there's another type of question or another, um, question you guys have that you want me to work out, let me know. Okay. So the very first one is the provider orders 650 milligrams of Acetaminophen. So I'm just going to write, oh right. Oh, is your order 650 milligrams of Acetaminophen available on hand is 325 milligram tablets.
So then the question is how many tabs do you give per dose? Okay, so there's our first problem, but ordering is a 650 milligrams of Acetaminophen. The available, uh, form is 325 milligram tablets. How many times are we gonna get, okay, so step one, step one, start with what you're looking for. Okay. So what are we looking for in this case? What are we looking for? What units? Tablets. Exactly. Tags. And you can even, if you want to just be really clear, you can say tabs per dose cause that's what you're asking, right? How many times are you going to give in this dose? So you start with what you're looking for and write that down on the far left and then you're going to put an equal sign. Okay? So this is step one. Step one, start with what you're looking for. Okay? So step two is transfer units across there. Up. So in this case we're going across, so we're going to take these tabs and transfer them over to it probably did transferred over tabs.
Okay, so now the question is what do, so step two was transfer units. Step three is insert, you know, convert. If you don't, what do we know about tabs or tablets? What do we know? We know that one tab is how much? Yeah, 325 milligrams. So we know one tab is 325 milligrams. Sorry. I like colors. Yo. So we know that one tab is 325 milligrams, right? So step one was start with what we know. Step two is transferring units across set three was insert what we know or convert if we don't set four is repeat steps two and three, right? So step two is transfer your unit across their up. So in this case we're going to transfer our units up to the next line. Okay, so transfer units. The next step, repeating, set three, insert what you know or convert. If you don't, what do we know? What other information do we know about milligrams?
So we've already used this one. Yes, our order is for 650 milligrams per dose, right? In one dose is 650 milligrams. Okay? So we transferred our units, we inserted what we knew. Remember our goal here is to cancel our units as we go. So anytime you have the same unit on the bottom and on the top, you're going to cancel it. So look, I've got milligrams here, milligrams here, so I can actually cancel those out, right? So the goal now is to cancel units until I achieve my desired result. Well, this is my desired result, right? So I've got tubs here, I've got dosed here, I've got what I want, right? I've got tabs on the top dose on the bottom, everything else is canceled. So now I can move on to step five. Step five is multiply across the top, divide across the bottom.
Now when I do this, this is all going to go into your calculator as one calculation, okay? Don't leave out your ones. Your ones will help you stay on track, right? So this is going to go in my calculator like this one times 650 okay, so I multiplied across the top. Now I'm going to divide across the bottom divided by three 25 divided by one. Again, multiplying and dividing by one doesn't change your calculation, but it helps you stay on track. Make sure you've included everything right? So I multiply the top divide across the bottom, all in one calculation. Put that in my calculator and what do I get? Easy part. Yeah. One time, six 50 divided by three 25 divided by one, two. And what are my units, tabs or tabs per dose. So even for these really simple problems, you can use dimensional analysis, which is nice. Questions about this one.
What we're going to do now is we're going to do correct Sarah. So by doing this in one calculation, Sara said, do we we divide across the bottom, not multiply? Yes, because we're doing it in one calculation. Well, some people will do is they'll multiply the top and multiply the bottom and then they'll divide them. I don't like that. That's multiple calculations. I don't want you to have to do that by going this times this divided by this divided by this you go one calculation, you've got everything. Cool. All right. So what we're gonna do now is we're actually gonna do a little bit of a more, um, a complicated problem, couple of extra variables. Um, but what it's going to allow us to see is how, not only can we use this for the really simple problems, we can actually use it for the more complicated problems as well.
All right. So our second problem is the provider orders 60 milli equivalents of potassium chloride ivy to be given over four hours. Okay, so that's my order. 60 million equivalents of potassium chloride ivy to be given over four hours. Kay? My available on hand is 100 milli equivalents of potassium chloride in one liter of normal saline. Okay, so order 60 milliequivalents over four hours available a hundred milli equivalents in one liter of Venice. The question says, what rates do you set the Ivy pump at? So here's a pop quiz for you guys. What units are we looking for? If we're looking for an ivy pump rate? Yeah, milliliters per hour, no, in some, uh, like syringe pumps and Nicky use, things like that. You might actually program milliliters per minute, but it's pretty rare. Nine Times out of 10 where we're looking for a raid on the pump, we're looking for milliliters per hour. So set one start with what you're looking for. So all the way to the left, I'm going to write milliliters per hour equals Kate. That's the very first step. So that's what I'm looking for. Step two is transferring your units across her up. In this case, we're going to go across and we're going to put milliliters. Okay? Now the next step, step three is insert what you know, convert. If you duct, is there anything in our question that we know about milliliters specifically?
Did we see milliliters up here anywhere? We don't, right? Nope. But what do we see? Yeah, we see that leader. So answer what you know or convert if you don't. So we need to convert these milliliters to leaders. So, uh, you guys got it right there. There's a thousand milliliters in one leader. And now I will tell you guys, I highly recommend you leave whole numbers here. Don't do, uh, like one milliliter is 0.001 liters. You're going to get your brain all mixed up. So a thousand to one is way easier to do than the other way around. Okay? So a thousand milliliters in one liter. Perfect. So the next step is transfer our units. In this case up, Kay. And now we can say, what do we, so we transferred units into or what, you know, convert. If you don't, what do we know about leaders? Now we have something, right? What do we know about this one leader here
that one leader has? Yup, a thousand milli equivalents. I'm sorry, 110 million equivalents of potassium chloride. Now before we move on, remember the whole goal here is to cancel our units til we get what we need, right? We've got leaders here, we've got leaders here. Let's go ahead and cross them off. Are we where we need to be yet? Not Quite. We still need hours, right? So I'm going to take these milliequivalents and we go back to step two and I'm going to transfer my units up. So now I have milli equivalents. So what other information do we have about our milli equivalents? We've already used the 100 so what else do we know about Milli equivalents? Okay, yeah. Want it is 60 million equivalents. And what do we know about that? 60 million equivalents. 60 million equivalents. Oh, her four hours, right? Do you guys see that? That is what is associated with that 60 million equivalent. So 60 over four hours. You're not slow. I'm fast. It's all good. All right. So again, our whole goal here is to get to the units we want. Okay. And so we have milliequivalents, the bottom and the top. So we're going to cross them out. So have we gotten where we wanted to be yet?
Okay.
We've got milliliters here, we've got ours here and that's exactly what we wanted, right? So we're good. So now we can move on to step five which is multiplied across the top, divide across the bottom. I'll write this one out cause it's still only have a few of them. Next one I won't be able to write out. So a thousand times one. Again, I leave my ones in because it just helps me place hold. Right? Make sure not miss anything. Times 60
okay.
Divided by one.
Okay.
Divided by 100
yeah.
Divided by four. All of that in your calculator at one time. 1000 Times one times 60 divided by one divided by 100 divided by four. And what do you guys come up with?
Okay.
What'd y'all get when you put that in your calculator? Yeah, 150 milliliters per hour. Now, in anytime you do dosage calculation of any kind, always go back and ask yourself if it makes sense. So if you had ended up with like 300 milliliters an hour, you'd be like, wait a minute, that entire leader's gonna be gone in three hours. Right? And that's way too much. So always kind of ask yourself if it makes sense. All right, so again, even as we get more complicated, even as we have conversions, even as we have more variables, dimensional analysis still works. And that's why I like it too. I like it. All right. Questions about this one before we move on to an even more complicated one? All right, so again, multiple variables, multiple conversions, we can do all of it. All right, so ready. Your patient has dopamine infusing at 39.3 milliliters per hour. So that's the first thing we know. Dopamine is infusing at 39.3 milliliters per hour. Our bag of dopamine has 400 milligrams from like blocking my face, 400 milligrams in 250 milliliters. Okay. My patient weighs 192 taps.
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okay, so the question is what's the dose they're receiving? Well, in dopamine we want to know many micrograms per kilogram per minute they are receiving. Okay? That's the standard kind of way we dose dopamine, Mikes per kilo per minute. So step one is always start with what you're looking for. Now here's the trick you need to learn. Anytime you have extra purs per kilo per minute, they both go on bottom, okay? So we're going to go micrograms on top and then we're going to go kilograms per minute on bottom. Okay? If you have a double part, they both go on the bottom fair. You'll get that. Cause that's really big. We're going to see that here in a second. It's going to be important. Okay, so step one, start with what you're looking for. Sarah. Sarah. Whoa. Do you need me to say it again? Stop me. Feel free to
[inaudible].
Okay. Okay, so nope, don't stop. Just cool. So micro grams on top, kilos per minute on the bottom. Okay, so step one, step two, transfer your units. So we're going to transfer our micrograms over. Step three, insert what you know, convert. If you don't, do we know anything about micrograms or do we need to convert something? Do I know anything? So Christopher, look, 400 milligrams. 400 milligrams. Yep. So we need to convert, right? So just take your time, right? There's no rush. So how many micrograms in one milligram? We're going to convert micro grams to milligrams. How many micrograms in one milligram? Yeah, a thousand again, always do a thousand to one. Don't do the point. Zero zero. That's too much. So a thousand micrograms in one milligram. Then we're going to transfer our units up, milligrams. And we already pointed it out. What do we know about milligrams? There's 400 of them, right? And how many? 400 of those milligrams in what? [inaudible] 400 milligrams in. You'll see it. Yeah. 250 milliliters. All right. I love the colors. You guys. I get a little crazy. So again, our whole goal is to cancel our units until we get to what we want. So since we have milligrams on the bottom milligrams on the top, we're just going to cross them off. We don't need them anymore. We're not where we need to be yet. So we're going to have to keep going. So we're going to transfer that unit up and we're going to put milliliters on top.
So now what do we know about milliliters? We've already used this one so we can't use that one anymore. So what else do we know about milliliters?
Okay.
Yeah. 39.3 so 39.3 milliliters in what? What is the 39.3 milliliters associated with
one hour? Exactly. To see how you see the things that are associated with each other. Right? One hour. So again, milliliters on the bottom, milliliters on the top, cross them off. All right, so now we're ours. Are we where we need to be yet? We don't need ours. Do we? What do we need? We need minutes instead. Right? So I'm going to transfer my hours up to the top. Sorry. I know this is going on two lines. That's okay. So I'm a transfer my hours up to the top and I'm trying to get two minutes. Right? So if I'm trying to get two minutes, I know one hour is how many minutes does the easy one guys then give me one hour is 60 minutes. Exactly. All right so I can cross off my hours cause I like hours there and hours there. So I've got my micro grams of gum. A minutes. What am I still missing? What am I still missing? And my problem?
Yeah, my kilograms. Okay. So here's the part where I'm going to slightly blow your mind and that's okay. That's okay. We need kilograms, right? And we need it on the bottom, don't we? Cause that's where we put it, cause we had our double Pur. So we need kilograms and we needed on the bottom. So we're going to put it there and then we're going to do what we gotta do with it. Right? So do we know anything about kilograms up here? Nope. We need to convert. So what's my conversion? What's my conversion from kilograms to pounds? Yeah. One kilogram is 2.2 pounds. So I have to make sure all of my units canceled. Right? So how am I going to get these pounds to cancel? I need another pounds on the bottom right cause otherwise I'm have microgram pounds per kilo minute. Right? Which is crazy. So I've got to get my pounds to cancel. So what do I know about pounds that I can get rid of?
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yeah, my patient, we use 192 pounds. Now this is the part, like I said, sometimes this blows people's minds, but if you just need to put an imaginary one in here, that's fine. Okay. Just an imaginary one. It's just a place holder. But now we've got our pounds in our pounds and we can cancel those. Now we've got our kilos on the bottom, micro grams per kilo per minute and we're ready to go. Stares. Mine as blow, let it. And then so really we did a calculation for the rate and then we realized it was weight-based. And so we added the weight part, basically what we did. So we've got everything we need, we've gotten to the units we were looking for, and now we can put it in our calculator. So I'm not going to write it out this time. I'm just going to draw it. So we're multiplying across the top and we have to our top come down here, right? So we're going to go in your calculator. Ready? 1,000 times, 400 times 39.3 times one times 2.2 times your imaginary. One K divided by one divided by two 50 divided by one divided by 60 divided by one, divided by 192
okay, so multiply everything across the top and then divide, divide, divide, divide across the bottom one calculation in your calculator. What do you come up with? Yeah, so your calculator will say 12.00833333. In our pumps, we only go to the 10th place. So if you round to the nearest 10th place for your pump, you're just gonna end up with 12 milliliters per hour. I'm sorry, 12 micrograms per gig. That was me as me, guys. 12 micrograms per kilogram per minute. We typically only go to the 10th place. So it'd be 12.0 is that 12 mics per kilo per minute will end you up at 39.3 milliliters per hour. Okay. So that one's a little more complex, has a lot more variables, lots of conversions that we have to do the double par on the bottom. But you see how we can do dimensional analysis for this super easy acetaminophen problem and all the way through these weight based problems that you have. Okay. So what question there? You're so excited and it's making me so excited. I love it. What questions can I answer? Is there another type of problem that you're not sure about? Um, questions about dimensional analysis. Anything goes? It's CALC.
Okay.
I just love math. I'm kind of a nerd. Math is fun, but honestly that's one thing I love about dimensional analysis is it doesn't really require a lot of math knowledge and thought it just knowing how to set it up. Um, so again, start with what you are looking for. Transfer your units, insert what you know, convert. If you don't add, repeat those two things until you cancel out everything but what you need and then you just do your math in the, in the calculator. It does. Absolutely. And so I'm going to send you guys a link really fast. There is a, I'm sorry I didn't have this open and I usually do. So this is my fault guys. Um, there is a lesson on dimensional analysis. We're actually work through the same three problems, um, but you'll be able to see me talk through it in the same way that I talked through it just now.
Um, and in there there's also a, excuse me, there's also a, um, TC on dimensional analysis with problems actually worked out in the dimensional analysis format. So you can see the way it's set up, you can see the order in which I went through. Um, and I'll actually give you a link to the library so that you can get that to cheat as well. So for those of you who are not in chat or don't have access to the library, if you go to the pharmacology course, go to module two, lesson two. It's a dimensional analysis lesson. And inside that lesson you will be able to download this cheat sheet that actually will give you, and I'll show you what it looks like. Um, it gives you examples of problems worked out. So there's the actual problem and then they're actually worked out in dimensional analysis so that you can see, you can even walk through and cross off the, uh, units and see where everything's at.
Um, and see how that was worked out. Okay. So any problem that you have, we have a ton of math. If you go to, in fact what I did that link to the library is farm module two, the math module, and then all of the cheat sheets that you can find there. So any problems that you have, use this method to work them out and see how accurate it is. Um, but really just knowing this steps to dimensional analysis and knowing how to set it up, that's really the best, um, thing that you can learn. Because then the math itself, the math works itself out. Right?
Okay.
Yes. So Chris had said it. Uh, it helps to set it up what you have versus what's available or what your order is. So I almost always write that way, my order or what's going on, you know, my available forms. I just get all my information kind of concisely in one place. Um, you will in nursing school, not on the end clicks maybe and then clicks, but very rarely, um, you will sometimes have information that's extra. So there is sometimes where you have to look and say, okay, do I even need this? Is this actually applicable to what I'm looking for? Is this the right piece of information? Um, so there's some critical thinking involved, but for the most part, if you follow that process, it really helps. It really helps.
Okay.
All right guys, any other questions? Yeah, they do. They do. The truth is, guys, I'm not, I don't like, uh, the things that are distracting for the sake of being distractors. But here's the reality. In real clinical practice, you're going to have all that information too, right? You're still going to have to pick which information to use, which numbers to use in the real world. You're going to have lots of numbers coming at Ya, you have a lots of information in a real clinical world. Um, and you do have to be able to pick out which information do I actually need. So this is like the one case like dosage calc is like the one case where I'm not super against it. Um, because in the real world you're going to have a lot of extra information too. So, but again, kind of understanding where you're going with things, understanding that you're trying to associate two things so that you can get your units canceled. Um, if you put a number in there but then you don't have anything to associate it with or it like doesn't, there's nothing you can say like, oh, that's equivalent to this many hours and that's equivalent to this many milliliters. It's possibly a piece of extra information. And so making sure that you're actually able to still follow that process is really helpful too. All right. Any other questions? Concerns, complaints?
Okay.
Awesome. Well you guys did awesome. I am going to post as always our little survey. Yes, CRISPR practice, practice, practice. It really, really helps. So that a library link with all the math teachers, pick any math, teaching any math problem, and use this method for it and get really good at this method and you'll be great. I like can't do it as attack any other way. All right guys. So fill out that survey for us. Let us know how we're doing. Let us know what we can do better. Um, especially if you have new ideas and new things you want to see us do sessions on and uh, we'll take it the happening for you. Alright guys, have a fabulous day. Go out and be your best valves and as always, happy nursing.