 So we're going to talk about unit conversions. And the first thing is just what do we mean by unit conversions? It's when you can convert from metric to metric, US to US, or you could also convert back and forth between metric and US. And there are two methods that I'm going to show you, proportions and also unit canceling, which is known more commonly as dimensional analysis. So in the first example, we're being asked to convert 150 milliliters to liters. Now I have already given you here the conversion factor, but this is something that you would have to come up with that 1,000 milliliters is equal to one liter. So starting with doing this using a proportion, I'm going to start with the question, which is we're trying to go from 150 milliliters to liters. So 150 milliliters. And then I'm trying to find liters. So I'm just going to call that x, what I'm searching for. And then we're going to set that equal to the conversion factor. Well, the conversion factor is 1,000 milliliters equals one liter. So remembering with proportions, it's really important that the units batch up. I'm going to make sure that the 1,000 milliliters is on the top, because on the left-hand side, 150 was milliliters. And in the bottom, I'm simply going to put the one liter. So again, what's in black here is simply the conversion factor. And then we're just going to cross-multiply. So 150 milliliters times one liter. And then we're going to set that equal to x times 1,000 milliliters. And then to solve for x, very simply, we're just going to divide both sides by 1,000 milliliters. And I'm going to look first off for units that will cancel out. I see I have milliliters on top and milliliters on the bottom. So on the left-hand side, I know that the unit, the only unit I'm left with is liters. And then let's multiply the top part. So 150 times one is 150. And in the denominator, I'm simply left with 1,000. And we'll come back in just a minute and simplify that further. On the right-hand side, 1,000 milliliters will cancel top and bottom. And I'm left with x, which was what I was trying to solve for. So grab in my calculator. Or you can do it in your head. 150 divided by 1,000 will give you 0.15. So I know that x is equal to 0.15. And I already have my units in place, so liters. So I know that 150 milliliters is equal to 0.15 liters. Now I'm also going to show you how to do this using dimensional analysis. So using dimensional analysis, what you do is you start with what's given, which is 150 milliliters. And basically, you're going to be multiplying that by something to get what you're looking for, which is liters. So the first thing you have to do is figure out is there a relationship between milliliters and liters, which I've already written here for you. So 1,000 milliliters is equal to one liter. Well, in dimensional analysis, your goal is to get the units to cancel. So again, I'm going to use this conversion factor, but I'm going to use it in a different way than I did with proportions. With proportions, if I had milliliters here, I had to have milliliters here. With dimensional analysis, you want your units to cancel out. So I have 1,000 milliliters. I don't want that in the numerator. I want that in the denominator. And my reason for that is I want these milliliters to cancel. There's one in the top and one in the bottom they will cancel. So that will leave me with the one liter in the numerator. So multiplying and canceling here. So first off, what can I cancel? I have milliliters in top. That will cancel with the milliliters in the bottom. And then we can just multiply straight across. If you need to, you can put the 150 milliliters over 1. But 150 times 1 liter will just give me 150 liters. And in the denominator, 1 times 1,000 is simply 1,000. And you see we're ending up in exactly the same spot we did in the last problem. And we know that 150 divided by 1,000 is going to give us 0.15 liters. So same exact scenario. Now in the next couple problems, I'll do some proportions and some dimensional analysis. So example two, we're going to do this one using a proportion. So convert five yards to feet. All right, so using a proportion, just start with initially what you have. So I have five yards. And I don't know how many feet. So yards on top, feet on the bottom. And then we're going to set that equal to the conversion factor. Well, this conversion factor is something that you should know. I already have it up here. But you should know that three feet will equal one yard. So three feet, one yard. One of them is going to go in the top, one in the bottom. With proportions, whatever is in the top has to be the same across. So I have yards in the top here. So I'm going to take that one yard and bring that with me. And then the three feet would have to go in the denominator. It would definitely not work if you flipped it. So we're going to cross multiply. So five yards times three feet equals x times one yard. And then again, to solve for x, you're simply going to divide those sides by the one yard. And when you do that, you'll have some things that will cancel. Here, the yard on the top will cancel with the one on the bottom. And you're left with, in the numerator, you're left with five times three, which is courses 15. When you divide that by one, you're still left with 15. So I'm going to go ahead and write 15. And our unit is feet. And then on the right-hand side, both of the one yards will cancel, because I have one top and bottom and I have x. So I have found that five yards is going to be the same thing as 15 feet. And again, we solved this using a proportion. Now, the third example, we'll do this one with dimensional analysis. So convert 13 miles to kilometers. And I have given you this conversion factor between miles and kilometers. You always want to start these problems by finding the factor that puts these two pieces together. I mean, that's where you need to start always. So doing this with dimensional analysis, you're going to start with what you're given, which is the 13 miles. And then you're going to be multiplying by something. And your goal here is to make sure that units will cancel top and bottom. Basically, I'm wanting miles to go away and I'm wanting the kilometers to stay. So how can I do that? Again, I'm going to use that conversion factor always. And that conversion factor have 0.62 miles equals one kilometer. If I'm trying to get rid of miles, I want miles on top and miles in the bottom. So I'm going to put the 0.62 miles in the bottom. And I'm going to put the one kilometer in the top. Again, the reason for that is to make sure that things will cancel. So if you will notice, I have miles on the bottom and top that will cancel out. And then I can simply multiply straight across. Again, if you want to, you could put this 13 over 1. So 13 times 1 kilometer is just going to be 13 kilometers. In the denominator, 1 times 0.62, of course, will give us 0.62. And then using my calculator, 13 divided by 0.62 will give me approximately 20.97 kilometers. So I know that 13 miles is approximately 20.97 kilometers. So example four, we're going to also do this one with dimensional analysis. And it has two parts to it. So we're trying to convert three feet to centimeters. So we could use a conversion that went straight from feet to centimeters. But what I'm going to do is go from feet to inches and then inches to centimeters. So you can see how to work when that requires two steps in it. So first off, I'm going to take the feet and try to convert them to inches. So I have three feet that I'm starting with. And I know with dimensional analysis that I need those units to cancel out, I'm going to use this first conversion factor, 1 foot equals 12 inches, to help me. So I know that the feet must go on the bottom because they must cancel out. The 12 inches is going to have to go in the top. So let's look at what will cancel. I know the feet in the top will cancel with the feet in the bottom. And then multiplying straight across, 3 times 12 will give me 36 inches. Dividing that by 1 doesn't change anything. So I'm going to leave that just as 36 inches. So my goal was not to find inches. My goal was to find centimeters. So I'm going to start with my 36 inches. And I'm going to see now if I can change inches into centimeters. So using my dimensional analysis, and I'm going to multiply by something, I know that I want my units to cancel. Using the second conversion factor, which says one inch is equal to 2.54 centimeters, that can possibly help me to finish the problem. So the one inch must go in the denominator so that the inches will cancel. The 2.54 centimeters will go in the numerator or the top. So what will cancel, the inches will cancel. And I'm left with centimeters, which was the whole purpose of the problem. If we multiply straight across, 36 times 2.54 will give us 91.44 centimeters. So I now know that three feet is the same thing as 91.44. And that sums up unit conversions.