 Hey you guys. So this week's lab we were looking at microscopic things, very small things, and so we talked about, and we had some problems that dealt with converting units, converting from something familiar like a meter to something maybe unfamiliar like a micrometer or a nanometer, which really when we were looking at the cool cells or the microscopic structures, we were looking at things that were the size of micrometers or micrometers. So there were some problems in the lab that dealt with converting between different units, and that process is called dimensional analysis. And for some reason it's tricky for students, but really it's not that tricky. So if you are having math phobia and hyperventilating, because you're about to do some math, stop, because it isn't crazy. So dimensional analysis is all about converting units. And the fact is those of us in the United States, we use some very strange units. We do not use the metric system. The metric system is logical and makes sense. And we use like whatever our English system is that's rather odd and sometimes doesn't make as much sense. But in the sciences, we always use the metric system. So being able to think through the conversions between the English system and the metric system, that's really helpful. And being able to think through big things and small things is also a really helpful place to be comfortable converting units. So I think I already said it's not crazy. So deep breath, converting units requires just one thing. It requires something called a conversion factor. And depending on what units you want to convert, that's going to determine what conversion factor you're going to use. All conversion factors, there's like jillions of them. So anything that you wanted to convert, you can do it if you have a conversion factor between the two things and all of them present two equal amounts. Did you follow what I just said? So I'm going to give you an example of a conversion factor and it is a factor that will tell you how many centimeters are in an inch. This conversion factor says one inch is equal to 2.54 centimeters. This, I don't know why, but I like putting my conversion factors in boxes so that you can visualize, like this is a thing, this is a tool. Conversion factors, okay, think about this for a second. What is that actually equal to? One inch and divided by 2.54 centimeters, do you agree that like actually, those are exactly the same length and therefore a conversion factor equals one. If you divide an inch by 2.54 centimeters, you've divided an inch by an inch because they're equal. So your answer is one. All conversion factors, they're not really fractions. They're ways of writing the number one. That's cool, that's easy. Because we can write a conversion factor, it just equals one, a conversion, this conversion factor can be written in another way. You can also write it 2.54 centimeters over one inch. Here's another like version flavor of the exact same conversion factor. The one that you're going to want to use, I will show you the strategy that you need to decide which one you want to use. But know that if, and most of the time people don't put your conversion factors in this form for you, but they'll put it like this. They'll say, hey man, one inch is equal to 2.54 centimeters. That's a conversion factor. I like to draw them like this because they're more helpful that way. Any time you see anything like this, if you've got an equal amount here, then you can turn that into a conversion factor. All right, shall we try a problem? Okay, I'm going to show you how we do this. You are going to tell me how many centimeters are in 10 inches. This is just a problem. Okay? When you set up your conversion, you're given a number that's a known number. Okay, so you are given 10 inches. And then you're going to multiply 10 inches by a conversion factor. The question is, I have, dude, two conversion factors right here. It's actually one conversion factor in two different flavors. And I know that one's going to work for me, right? Because I've got inches and I want to get to centimeters. Look, this is a direct shot. I've got inches, it's going to get me to centimeters. Fantastic. But you might be wondering, which one do you use? Here's the fact. This is why I set up my conversion factors this way. If you have inches and you want to convert to something else, you've got to get rid of the inches. The inches, do you agree that this is actually like putting it over one? So the inches are on top, they're in the numerator. So if you want to get rid of them, how are you going to get rid of an inch? How are you going to get rid of those units? You've got to put it on the bottom because then what happens? They cancel out and that's actually equal to one. But what is that, you can't just say, oh, I want inches on the bottom. We do have a conversion factor that'll take us to centimeters and now you figure out which one of these is it, this one? No, because that has inches on the top and centimeters on the bottom. This one, 2.54 centimeters is equal to one inch. Now here's the cool part. You're done because look, I canceled out my inches and now the only units that are left are centimeters. That's what I wanted to get into anyway. That's where I wanted to go. Now you just do the math straight across. This one's super easy because all I have to do is multiply 10 by 2.54 and that means I'm going to get 25.4 centimeters. Sometimes you have to multiply the numbers on the bottom and do a division problem, no problem. In this case it's easy, one times one is one and one divided by 25.4, 25.4. No, I said that wrong. 25.4 divided by one is 25.4, which is that problem right there, which means what's your answer? 25.4, okay, you good? The key to doing this is making sure that you have conversion factors that work for you, that you understand an equal part to an equal part. If you think about this, if one inch is 2.54 centimeters it makes sense that you're going to have in 10 inches more centimeters than you had inches, right? So it makes sense, 25.4 is the number that makes sense. Let me give you another one. What if I said I had 10 centimeters and I wanted to know how many inches that is? Do you see how I just made a totally different problem? So don't be confused, this was problem number one. Now I'm going to rock problem number two. Is this time, can I set it up the same way? Let's look, 10 centimeters, I know I'm going to divide it, or I know I'm going to deal with a conversion factor, okay? But what unit has to be on the bottom of my conversion factor so I can cancel out my centimeters? I have to have centimeters on the bottom, which conversion factor am I going to use? So this one, 2.54 centimeters is equal to one inch. Now you might be like, ah, it looks different. But it doesn't really. Remember this was over one, or what we start with is over one, 10 times one. We canceled out our centimeters so now we have the units that we want inches. 10 times one is what? 10, I like those math problems. 10 inches divided by one times 2.54, which is 2.54. Now, if I were amazing, I would totally be like boo, and I would tell you what that was. And I'm not amazing, I bet it's around four, right? Something around there. And you can get, grab your calculator and do the math, 10 divided by 2.54, and then you're going to get a number here and that's going to be the number of inches. I sort of feel like I should finish it for you, but I kind of want to keep going. Are you good? All right, so what's the only thing you need to convert between units? You're going to need conversion factors, that's it. And here's what I can tell you in Wendy Land. I will always give you conversion factors that you need. If you are in chemistry land, so I'm just going to throw this out there for you two home dogs who might find this helpful. If you're converting between things on the periodic table, all you'll need is a periodic table to convert between grams and moles and things of that nature in chemistry land. And again, it isn't hard, you just have to know what conversion you're actually going to be using. Okay, I want to show you something. Let me, let's see, what was it? I thought I, oh, there. This is why I'm doing this video because, look, these are conversion factors and they look weird, don't they? Where it says one millimeter is equal to 0.001 meters or 10, one times 10 to the negative three meters or 1,000th of a meter. That's all, that's giving you information that you can use to build a conversion factor. And so I'm going to just, I want to make it a little easier because look at our prefixes there. We've got a meter and then we get small. We go millies, micros and nanos. And that's like how we're not really getting, not getting smaller than that. Millies, micros and nanos. So let's go and I'll show you the conversion factors that, what that actually was telling you. I think it's easier to think one meter is equal to one times 10 to the third millimeters. This is my milli. You could also, now that means that my conversion factor is going to look like this, one meter over one times 10 to the third millimeters or one times 10 to the third millimeters over one meter. Or I want you to, no, I'm not going to do it as an or. I'm going to do it as, there's another way we could say this. We could actually say one millimeter is equal to how many meters? And this one, I mean, it's just another conversion factor. Look at what I did. What do you notice here? The one millimeter is one thousandth of a meter and this is another legit way to do a conversion. I think that math, when you're dealing with negative exponents, it just means that you have a 0.12, oh geez. We started with one, we went one, one, two, three, which means I've got two zeros. I got there, it's all good. That is all that is. It's kind of nicer to look at a thousand. I don't know why that's nicer, but it's a little bit less intimidating. Negative exponents can be a little daunting, but it's the same thing. So it really doesn't matter. You're going to get the same answer whether you use this conversion factor or this conversion factor. And then I'm going to give you another one. One meter is equal to one times ten to the sixth micrometers. So that's my micrometer. And often, micro, it's led by that guy, which is, it's called mu. It's a Greek letter and it kind of looks like a U sometimes, but it actually is a cursive M symbol. And the other one that we have is, and again, you can throw it into all of that format. Any one of those is going to work. One meter is also equal to one times ten to the ninth. Was it picometers? Picometers. Was it pico or was it nano? I feel like it was nanometers. I got to go look. It was nanos. Silly nanos. Pico's must be 12. Look, I'm going to throw that in there just for the heck of it. 12 is picoland, but I'm going to give you the nanos. One times ten to the ninth nanometers. Here's the scoop. On any kind of exam or anything, I'm going to give you the conversion factors. You don't have to memorize any conversion factors. I do expect you to be able to tell me if a millimeter is bigger or smaller than a meter. Micrometers, bigger or smaller than a millimeter and a nanometer. Picometer I just threw in there because I made a mistake. All right, what do you need to know? Oh, I know what I want to show you. I want to show you another one because this is fun. Don't ever forget it. I want to show you this one. This is one that was actually on your lab. This was 1.2 millimeters is equal to how many micrometers. Now, there is in all of our lab material, we don't have a conversion between millimeters and micrometers. You can look at the lab material and you can be like, dude, if a millimeter is, if there's one times 10 to the third, if there's 1,000 millimeters in a meter and there's a million micrometers in a meter, there's actually 1,000 micrometers in a millimeter. You can logic that through but you don't have to. If you're like, huh, what did she just say? You can actually use two conversion factors here. So all I'm going to do is I'm going to take them both two meters. So watch this. I know that one meter, because I just did this, one meter is equal to one times 10 to the third millimeters. Okay? There's my millimeters. I also know that one meter is equal to one times 10 to the sixth micrometers. Now, this is a bit of a longer way to go, but you're going to get the same answer. So watch what happens. Now we're going to lay out our conversion factors. And I know right off the bat that ultimately, I want to get to micrometers over here, but that's not going to get me there. In order to use this conversion, I'm going to have to go to meters first. So look, I've got a conversion factor that I can use to get from millimeters to meters. What goes on the bottom? What format? Nice. It actually goes in this format because millimeters goes on the bottom so I can cancel it out. I've got one times 10 to the three millimeters. That's equal to one meter. Now, I also have a conversion that goes between meters and micrometers. And micrometers is where I want to end up. So now I can say, okay, I know I already canceled out my millimeters, so now my units are in meters. Now I want to cancel meters. I'm going to throw meters on the bottom, right? And that's going to let me cancel it out. And I'm going to throw micrometer on the top because look, I've got a conversion. So what is the format of this puppy? I'm going to have to flip it, right? One meter is equal to one times 10 to the sixth micrometers. And then we do the math. Now, if you remember properly, everything here is a one, right? Everything, we're multiplying by one. We're dividing by one. Everything is a one except we're dealing with exponents. So I can actually take 1.2 times 1 times 1 times 10 to the sixth power, okay? Watch what happens there. It's just 1.2 times 10 to the sixth power, right? I have to multiply everything through the bottom. One times one times one times 10 to the third. One times 10 to the third power. Now dividing exponents really is not scary. Look into my eyeballs. It ain't scary, dog. If you're dividing exponents, you just subtract them. And so one divided by 1.2, I mean 1.2 divided by one is 1.2. 10 to the sixth divided by 10 to the third is 10 to the third. And my units that I'm left over with, the only thing that didn't get canceled out is micrometer. Boom. Look into my eyeballs again. You show your work. Just do it like if it takes longer to think it through, like who cares? That's awesome. It takes as long as you need to write out that whole process. And if we were amazing, we could have given you the fact that 1 times 10 to the third, oh, no, no, no. Here's another convergent factor. So the micrometer is equal to 1 times 10 to the third micrometers. And you could use that conversion factor in place of those two conversion factors. But you can also just throw two conversion factors and they're gonna be just fine. So how do you feel? I don't think it's crazy. I have a present for you. Well, okay, it's not really a present. This guy has a present for you. Who are these people? There's a whole walkthrough on this process of dimensional analysis. And so you can go there to that land and they will show you how to do all those dimensional analysis problems. Woo, woo. How you feeling, dogs? All right, that wasn't so bad, was it? How long do you think it was, like five hours? I don't like it. Okay, bye-bye.