7.6 – The SI Prefixes
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Now, one of the things that I promised you with the metric system, was that we were going to be able to have very, very large and very, very small units. The way that we get very, very large and very, very small units is by having prefixes that represent very, very large and very, very small powers of ten. The system of those prefixes plus the metric units is called the SI system. Now, SI does not stand for scientific, though it’s usually used in science. SI stands for System International, words coming in that order because it was originally a French standard. So, what are the SI prefixes? Here’s a list of some relatively commonly used SI prefixes as well as the corresponding powers of ten. A couple of things to be aware of in this list. You’ll notice that some letters appear twice, both as capital and is lowercase. Case matters. Make sure that you’re using the letter that you mean. Notice, that the prefix, deca, has a two letter abbreviation. And the prefix, micro, has this weird symbol, we write it stroke up that goes below the line, little u-shape, little tale that comes down. This is the Greek letter, mu. So, we read it as “mew”, like what the cat says. The Greek letter, mu, is the prefix for micro. Why is the prefix for micro a Greek letter? I really don’t know. So, all of these units here describe really big things or really small things. Some of these really big units, giga, mega, kilo, they might be familiar because we use them when we’re talking about computers. Tera is actually becoming more and more common. I know every computer I’ve gotten in quite some time has had a terabyte hard drive. Now, we use these in the same way that we use the everyday prefixes, but you’ll notice that really, really big numbers turn up. Keeping that in mind, working with the SI prefixes is much, much easier if we just work in scientific notation. Let’s see what we mean by that. Suppose, I told you that the thickness of a human hair is about eighty micrometers, that is micro-meters, and I asked you to tell me, what is that in centimeters? In order to make that conversion, I would first write that number, eighty, in scientific notation. The reason that I want to do that is that it’s going to make all of the arithmetic that’s coming up much easier. Now, I’m going to use a two-step conversion. I have eight times ten to the one micrometers over one times a conversion factor that’s going to get rid of micrometers and bring in meters. Times a conversion factor that’s going to get rid of meters and bring in centimeters. Now, the unit with the prefix always gets the number one. And then the base unit gets the number that the prefix represents. So, micro represents ten to the negative six. And centi represents ten to the negative two. So, I’ll have eight times ten to the one times ten to the negative six over ten to the negative two. And then micro meters cancelled out, meters cancelled out, I’m left with just centimeters. OK, well then let’s just do arithmetic with those powers of ten, right? Ten to the first times ten to the negative six is ten to the one plus negative six. So, that’s ten to the negative five. Ten to the negative five over ten to the negative two is ten to the negative five minus negative two. That’s ten to the negative three. So, just working out these powers of ten, this works out to ten to the negative three. I’m left with eight times ten to the negative three centimeters. That’s a perfectly good answer. If I really, really, really want it in decimal notation, I can do that, too. I start with eight and move the decimal one, two, three places to the left. I have zero point zero zero eight centimeters. Notice, how the scientific notation made those decimal places really easy to keep track of. I could also have done that on my calculator. I could have said, eighty times ten to the negative six divided by ten to the negative two. And I would have gotten that same zero point zero zero eight. Very often when we make these conversions with SI units, we end up with our answer in scientific notation or else we started off with our answer in scientific notation because it was a huge number. For example, suppose we’re told that the mass of the sun is about one point nine eight nine times ten to the thirtieth kilograms and we want to say, what is that in petagrams? So, I think we need to check and see what the heck was peta? Peta, that was the ten to the fifteenth. So, one petagram is ten to the fifteenth grams. So, we set up our conversion factors. We’re starting with one point nine eight nine times ten to the thirtieth kilograms over one. And then we’ll have a conversion factor that will cancel out kilograms and bring in grams. And then we’ll have a conversion factor that will cancel out grams and bring in petagrams. The unit with the prefix always gets one. And then the base unit gets whatever the prefix represents. Kilo means ten to the third. Peta means ten to the fifteenth. So, kilograms cancels out, grams cancel out, and we’re left with petagrams. One point nine eight nine times ten to the thirtieth times ten to the third over ten to the fifteenth petagrams. So, let’s see, ten to the thirtieth times ten to the third is ten to the thirty-third, right? Adding together the exponents. Ten to the thirty-third over ten to the fifteenth is ten to the thirty-three minus fifteen. That’ll be ten to the eighteenth. So, I’ll have one point nine eight nine times ten the eighteenth petagrams.

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