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Welcome to the presentation on units. Let's get started. So if I were to ask you, or if I were to say, I have traveled 0.05 kilometers-- some people say KIL-ometers or kil-O-meters. If I have traveled 0.05 kilometers, how many centimeters have I traveled? That's question mark centimeters. So before we break into the math, it's important to just know what these prefixes centi and kilo mean. And it's good to memorize this, or when you're first starting to do these problems, you can just write them down on a piece of paper, just so you have a reference. So kilo means 1,000, hecto means 100, deca means 10. You might recognize that from decade, 10 years. And then, of course, you have no prefix, means 1. No prefix. No prefix equals 1. deci is equal to 0.1 or 1/10. centi-- I keep changing between cases. centi is equal to 0.01, or 1/100. And then milli is equal to 0.001, and that's the same thing as 1/1,000. And the way I remember, I mean, centi, if you think of a centipede, it has a 100 feet. A millipede, I'm not sure if a millipede has 1,000 feet, but that's the implication when someone says a millipede because pede means feet. So let's go back to the problem. If I have 0.05 kilometers, how many centimeters do I have? Whenever I do a problem like this, I like to actually convert my number to meters because that's very easy for me. And actually, I'm going to abbreviate this is km, and we can abbreviate this as cm for centimeters. So let's say 0.05 km. Well, if I want to convert this into meters, is it going to be more than 0.05 meters or less than 0.05? Well, a kilometer is a very large distance, so in terms of meters, it's going to be a much bigger number. So we can multiply this times 1,000 meters, and I'll do it over 1, per kilometer. And what does that get? Well, 0.05 times 1,000 is equal to 50, right? I just multiplied 0.05 times 1,000. And with the units, I now have kilometers times meters over kilometers. And the kilometers cancel out. And just so you're familiar with this, you can treat units exactly the same way that you would treat numbers or variables. As long as you have the same unit in the numerator and the denominator, you can cancel them out, assuming that you're not adding units, you're multiplying units. So you have kilometers times meters divided by kilometers, and that equals 50 meters. And it's good to always do a reality check after every step. Usually when you do these types of problems, you know, OK, if I want to go from kilometers to meters, I'm going to use the number 1,000, because that's the relationship between a kilometer and a meter. And you're always confused, well, do I multiply by 1,000, or do I divide by 1,000? And you always have to say, well, if I'm going from kilometers to meters, I'm going-- 1 kilometer is 1,000 meters, right? So I'm going to be multiplying by 1,000. I'm going to get a bigger number. So that's why I went from 0.05, and I multiplied it by 1,000, and I got 50. So let's get back to the problem. 0.05 kilometers is equal to 50 meters. We're not done yet. Now, you need to convert those 50 meters into centimeters. Well, we do the same thing. 50 meters times-- how many-- so what's the relationship between meters and centimeters? Well, if we look at the chart, we see it's 100. And the question I'm going to ask you, am I going to multiply by 100, or am I going to divide by 100? Well, it's the same thing. We're going from a bigger unit to a smaller unit, so one of a bigger unit is equal to a bunch of the smaller units. So we're going to multiply. So we say times 100 centimeters per meter, right? And that just makes sense. There's 100 centimeters per meter. So 50 meters times 100 centimeters per meter is equal to 50 times 100 is 5,000, and then the meters cancel out, and you get centimeters. So what we have here is that 0.05 kilometers is equal to 5,000 centimeters. Let's do another problem. I think the more examples you see, it'll make them a little more sense. And always try to visualize what we're doing, the scale. Otherwise, it's very confusing whether you should multiply or divide. Let's say I have 422 decigrams. Grams are a measure of mass. One gram is actually a very small amount. That's what you measure-- I guess in the metric system, they measure gold in terms of grams. And I want to convert this into milligrams. So before we start the problem, let's just do a reality check. Am I going from a bigger unit to a smaller unit, or a smaller unit to a bigger unit? Well, decigrams, that's 1/10 of a gram, and I'm going to 1/1,000 of a gram. So there's two ways of doing this. We can convert to grams and then convert to the other unit. That sometimes make things easy. Or we could say, well, how many milligrams is equal to one decigram? Well, a milligram, as we see here, is 100 times smaller, right? To go from 1/10 to 1/1,000, you have to decrease in size by 100. So we could just say 422 decigrams times 100 milligrams per decigram. And then the decigrams will cancel out, and I'll get 422 times 100, 42,200 milligrams. Now, another way you could have done it is the way we just did that last problem. We could say 422 decigrams, we could convert that to grams. We could say 422-- I'm just going to say dg. That's not really a familiar unit-- decigrams. And how many decigrams are there per gram? If we're going to gram, 422 is going to be a smaller number of grams, right? So we could say times 1 decigram is equal to how many grams? Well, 1 decigram is equal to-- no, sorry. 1 gram is equal to how many decigrams? Well, 1 gram is equal to 10 decigrams. And the reason why this makes sense is if we have a decigram in the numerator here, we want a decigram in the denominator here. So if we have decigrams cancel out, 422 decigrams will equal-- that divided by 10 is equal to 42.2 grams. And now we can just go from grams to milligrams. Well, that's an easy one. 1 gram is equal to 1,000 milligrams, so we could say times 1,000 milligram per gram. The grams cancel out, and we're left with 42,200 milligrams, right? 42.2 times 1,000. Hopefully, that doesn't confuse you too much. The important thing is to always take a step back and really visualize and think about, should I be getting a larger number or a smaller number than the one I started off with? I think you're ready to now try some problems. Have fun!