 When I was going over the metric units, I said that there were variations on the metric units, so I said there was a gram, but there were variations of the gram, there were leaders, there were variations on the unit for leader, and we're going to talk about that now. Specifically what we are going to talk about is metric unit prefixes, so prefixes are the way that the units in the metric system are changed or modified, so before we get into what a metric unit prefix is, I just want to make sure that everyone understands what a prefix is, so we're just going to briefly talk about a prefix. A prefix is basically a piece of a word that you tack on to the front end of another word, and no matter what word you tack it on to the front end of, it changes the meaning of the word in the same way. The example that I am showing here uses a prefix that has the letters D and E. DE is a prefix that basically means take away from, and no matter what you stick the letters DE on to under certain circumstances, it basically changes the end part of the word in the same way by adding the meaning take away from. So if you devalue something, you take away value from something, which means you reduce its value. If you deconstruct something, you take construction away from something, which means you break it apart. So that's basically what the prefix D and with the letters DE does. It changes the meaning of many other words in the same way by applying the same sort of change to it, take away from. So the metric system has its own collection of prefixes, and the idea is that the prefixes in the metric system change the meaning of the unit in the same way, no matter what unit you attach the prefix on to. So before I go into what the prefixes are and how you use them, I want to explain why they're used. So the way that I explain why they're used involves actually units that are not metric. So usually what I do is I ask my on-ground students a couple of questions. Since I can't really hear your answers, I'm just going to pretend that I'm talking to myself, which I kind of am. The first question is, how tall are you? Well, I am 71.5 inches tall. And there's my number, there's my unit. Second question is, what's the distance from where I live to the grocery store? And I will say that it's about two miles. Again, I have a number and I have a unit. And what I usually do at this point is I ask the students, how come you didn't tell me how tall you were in miles? And people usually think this is ridiculous. And it is ridiculous, but it could be done. Instead of using units of inches, I could use miles. And I think I looked this up a while ago. I think I am about 0.00114 miles tall. So you can do it. The other question that is also a little bit ridiculous is how come I didn't tell people how far it was to the grocery store in inches? Again, most of the students think that's a little crazy, but it could be done. I think it is about 127,000 inches to the store from where I live. And again, so the question is, why do I use units of inches when I'm talking about how tall I am? I don't have to. I could use miles. And why do I use units of miles when I'm talking about how far it is to the store? And why don't I use inches? There's no definitive answer for this, but I think the answer I'm going to give is probably more or less correct. The reason why I think this is true is that the human mind is pretty good at understanding numbers that are between about, excuse me, between about 1 and 100 or 1 and 1000. We're pretty good at sort of counting in that range. If we go much less than one, it starts to basically hurt your head and make it hard to wrap your mind around what a number less than one means. And if we go much past 1000, it's also hard to understand how big that number is. So as an example, I kind of know what .00114 is, but it's not the easiest thing to wrap your head around. I know more or less what 71 and a half of something is, so this is relatively easy to understand. So the point of changing units, changing from inches to miles or miles to inches, is to switch the number that you get out to a more human understandable one. .00114 miles. I don't really know what that is. I don't have a deep understanding of that. 71 and a half I know what that is. Same thing with distance to the grocery store. 127,000. I know at least in theory what that is, but it's hard to really imagine what 127,000 of something is. Two, I know what that is. I know what a mile is more or less, and I know what two of them are probably going to be roughly. So the punchline here is that we switch units to turn the numbers that we're dealing with into more human understandable ones. Now these are English units or something related to English units, but the same kind of thing happens with the metric system. And so the metric system, however, uses prefixes to modify the units to make the numbers more understandable. And that's what we're going to talk about in the next couple of slides. Let's see. So the metric system, for example, uses a meter. One meter is one meter. That is about the distance from, let's say, your shoulder from here to about the tips of your fingertips. I know that most of you are, you know, everybody has a slightly different length of arm, but roughly that's about one meter. So this is going to be my meter stick. And you can measure the height of people using a meter stick. So Kobe Bryant here, he's about two meters tall. So it's reasonable to use the unit of meters when I'm talking about how tall people are. However, things get a little bit more problematic if I'm measuring the distance to the store or other places. As an example, if I want to go from Haverhill, Massachusetts to Kingston, New Hampshire, I'm going to pretend that it's 6,500 meters. So here's my meter stick again. And if I laid 6,500 of these end to end next to each other, maybe it tells me the distance between those two towns. However, as I mentioned earlier, 6,500, a little confusing. At least hard to wrap your head around once the numbers get too big. So what the metric system does is it says, look, I want to group a thousand meters end to end as its own special unit. And the way that I'm going to describe it is it's related to a meter. So the end part of the unit is going to be called a meter. But I'm going to modify the front part with a prefix called kilo. So excuse me. The prefix here is kilo. And kilo basically means take this unit meter and use it in groups of a thousand. And each group of 1000 meters is called a kilometer. And so instead of telling people that it's 6,500 meters between the towns, I can say that it's about 6.5 kilometers between the towns. And hopefully that is a little bit easier on the head to understand. You know more or less what six and a half of something is. 6,500 in theory, you know what that is, but it's hard to sort of get a good sense of of how big a distance that is. So that's what the metric system does is it tax these little prefixes on to the end of its standard units and the prefix. In this case, it's kilo, but there are other prefixes that are coming. Kilo basically changes the meaning of the end unit in the same way. Same thing. We can have grams. I told you that gram was a metric unit. We can have kilograms. If I put the prefix kilo in front of gram, that means use a thousand grams as your unit. So the reason it's called the prefix is I can put kilo in front of any of the metric system. I can put it in front of liter, things like that. And this means a thousand liters. So no matter what I tack kilo on to, it changes the meaning of the unit in the same way. Why it's called the prefix. Here's another example where you might want to go in the other direction. Again, one meter is one meter. And here is our meter stick over here. But pretend that we wanted to actually measure the length of a very tiny thing. So pretend this is B. And there's our B. And if we used a meter as a unit, our B is approximately 0.01 meters long. Again, this number is a little bit hard to deal with for the head. So if we can switch the units so that we end up with a number that's more human understandable, it will help us. And what the metric system does is it says, look, why don't I take the meter and break it into 100 even pieces. So pretend this is me breaking the meter stick into 100 even pieces. And each piece is called a centimeter. And centi is just a different prefix that you can tack on to different metric units. And it means break your unit into 100 even pieces. And then we can instead of saying that our B is 0.01 meters long, we can say that our B is about one centimeter long. And you'll notice that we ended up with a number one that's a little bit more easy for the brain to understand. So again, new prefix, we've gotten kilo, we've gotten centi now. Let's see, there are others. Oh, here's a different example. This is a picture of a bacterial cell. And if you wanted to measure the length of one of those cells, you can use meters and you can say the bacterial cell is 0.0000002 meters long. Again, this is really hard to understand what that number is. One way of dealing with that, let me show you the meter stick, is we could break the meter stick into a million even pieces. So pretend this is me breaking it into a million even pieces. And each of those even pieces is called a micrometer. Micro is the prefix that basically means break your metric unit into one million even pieces. And that's basically how it works. It doesn't just work with meters, it works with liters, it works with grams, works with pretty much any metric unit that I can think of. So let's see, where are we? So again, one meter is one meter. If we need to measure things that are much longer than a meter, we can group the meters into groups of a thousand and then the prefix is kilo. If we're dealing with something that's very small, we can break the unit into a hundred even pieces. The prefix is centi. We didn't cover this one, but if we want to break the unit into a thousand even pieces, the prefix is milli. And you notice that the abbreviations for the modified units are pretty easy to understand. Kilo is km, centimeter is cm, millimetre is mm. We just did micrometer. Micrometer, micro means break your unit into a million even pieces. The problem with the abbreviation for micrometer is that you want to use the letter m, but the letter m is already being used for milli. So because scientists are kind of nerdy and stuffy, they rated the Greek alphabet and found a letter that sounds like the letter m. The letter in the Greek alphabet is called μ. That's, I guess, how we spell it. It's written like this. It looks like the letter u with a little tail here. And so the correct unit for the correct abbreviation for micrometer is the Greek letter μ and then m. However, this is very hard to find on your computer, on your keyboard. So a lot of times scientists get lazy and they will use the letter u instead as kind of a quick and dirty substitute for the Greek letter μ. So you sometimes will see micrometer written with the Greek letter and sometimes you'll just see it written with a u because people are being lazy and they don't want to hunt down the Greek letters in the alphabet. And again, just to emphasize that these are prefixes, meaning that you can put them on to different units and they change the unit in the same way, kilo means group in groups of a thousand. I told you that a gram is about the weight of one paperclip. If I want to weigh things much more than a paperclip, I can use kilogram, which basically means weigh in groups of a thousand grams or a kilogram is roughly a thousand paperclips, or if I need to weigh something much smaller, I can break my paperclip into a hundred even pieces and each piece is called a centigram, or I can break it into a thousand even pieces. And each little piece of my paperclip is weighs about a milligram, or if possible, I could break my paperclip into a million even pieces and each piece is called a microgram. Again, these units show up over and over again, whether they're tacked onto meters, whether they're tacked onto grams, whether they're tacked onto liters, they do the same thing to the unit. So to summarize, what's the purpose of metric unit prefixes? Nobody wants to think about how many inches it is to the grocery store, even though you could do it. So what you do is you shift units to give you more understandable numbers. Instead of saying it's 127,000 inches to the store, I could say that it's 3,218 meters to the store. However, 3,218 is still a little bit confusing, which is why I'm writing question marks. So you can switch that as well and use kilometers as your unit. And then you can say, well, it's about 3.2 kilometers to the store. As long as you have a sense of what one kilometer is, it's not too hard to understand what 3.2 of them are. So that's basically why metric unit prefixes exist. I will tell you that you shouldn't memorize those prefixes. There are many more prefixes than the ones we went over, but those are the ones that show up the most often. Again, don't memorize these. I will give you that information on a quiz or a test, but you'll have to be able to use it. So for example, I might say there are 1,000 millimeters and 1 meter. So I'll give you that information on a quiz or a test, but you're going to have to be able to use it. So keep that in mind.