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Anderson Video - Converting Units (Area)

Professor Anderson
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 >> Let's talk a little bit about converting units when we're dealing with things like area. So, let's say, for instance, we wanted to calculate the area of a sheet of paper. But we want to calculate this in terms of square meters. Okay? How many square meters is one sheet of paper? Well, let's think about this for a second. Here's a sheet of paper. Okay? It is how big? 8.5 by 11 inches. How big is a square meter? Well, a square meter is 3 feet by 3 feet. All right? 3 feet here is probably about like that. This is about 3 feet tall. So how many pieces of paper will fit in this area? Well, one, two, three, four, five wide, by one, two, three tall. Maybe a little bit of extra somewhere. So, let's say that we're going to guess that it is a 20th of a square meter. We can take 20 pieces of paper and fill up a square meter. So, each piece of paper is roughly a 20th. And now let's calculate it and see what we get. All right. We said it's 8.5 inches by 11 inches. All right. So, that is 8.5 times 11. When I multiply two units I get a square. So, it's square inches. And now I have to convert that. So how do we convert it? Well, we just talked about going from centimeters to inches. Let's do that again. 2.54 centimeters per inch and now we want to get it to meters, and we remember that in 1 meter there are 100 centimeters. All right. So, we've got 8.5 times 11 times 2.54. And we're going to divide by 100. And it looks like we're going to end up with square meters. We had inches squared, but down here we only had inches. So, I could cross out one of them, but then I would still be left with inches up there. And so, in fact, I need to square that whole quantity. And now I'm going to end up with centimeters squared. And I have centimeters down here. So, I also need to square that whole quantity. And so, the numbers here are not just multiplied directly, then you have to square them. 2.54 is squared. 100 is squared. Okay? And now that should tell us how many square meters that is. I'll approximate it here if you guys want to punch it into your calculator and let's see what you get. So, 8.5 times 11, that's got to be close to 100. 2.5 squared is what? Well, 2 squared is 4. 3 squared is 9, and it's not quite halfway in between those, so let's say it is something around, how about 6? And then down at the bottom we have 100 squared. So, we will just leave that as 100 squared. Because look what happens. One of those 100s up there cancels with one of the hundreds down there. I get 6/100. 6/100 is 0.06. What did you guys get for your calculator? >> Same thing. >> Same thing? >> 0.0 >> All right. So, our guess was good. And that is pretty close to a 20th of a square meter. Right? A 20th is actually .05. But .06 is very close to that. All right? So, this is a good thing to do. Take a guess at what your answer should be when you face these sorts of problems. And if you get an answer that is completely off, orders of magnitude off, either your answer is wrong -- you missed on the math somewhere. Or your intuition was way off, okay? And so, you should adjust either of those things.