 This bootcamp takes you through several mathematical concepts and techniques that you need in order to do the introduction to statistics course. Sometimes your calculator displays something unexpectedly alien with maybe the letter E, a plus sign, a minus sign, and you're not really sure what to make of it. If you haven't seen this before, that's just scientific notation. It's a way to make a number with many digits more concise, and we'll see how that works. So don't worry about it, don't panic, it's quite normal. Scientific notation, as we'll see, can help us take a very, very large number and squash it into a calculator display that wouldn't be able to hold it otherwise. So here we have an example where we take 1, 2, 3, 4, 5, 6, 7, 8, 9, big number, multiply it by 99 to make it an even bigger number, and what does the calculator tell you? 1.222, 2222, 11, E plus 10, scientific notation. The calculator in the image over there doesn't even use the letter E, so you might be even more confused. Different calculators and different apps will give you different displays for scientific notation. But basically what we're told to do here with the plus 10 is go to the right 10 spaces, okay, 10 decimal digits over to the right. So the number starts out 1.2, we move the decimal point over and over again and over again to the right 10 times, and we end up with an answer like 1, 2, 12, 222, 222, 122,110. Of course that's not exactly accurate either, but it's close. Because of the constraints of the size of the display, we didn't have enough digits telling us what that the end of the number is, 110. It's really 111, but it's close enough, and if we needed to, we could keep the answer in our calculator or in the computer and manipulate it further in order to get a more accurate result altogether, that's if this is an intermediate result. But the whole point here is just to tell you, don't worry, scientific notation is easy to figure out. Let's see how scientific notation helps us with a very, very tiny number. We've got 0.03 raised to the power of 5. So that's 0.03 multiplied by itself 5 times. And the calculator output, as you see here, is 2.43 E-8, so that's scientific notation. We know that because of the E, but even if the E is not there, we'd be able to figure it out. And minus 8 means that it's a very tiny number. We're going to move the decimal point over to the left, not to the right. The minus sign tells us we're going to move to the left, 8 spaces. And we end up with, let's see if we can figure this one out, 0.000, 000, 0243, that's the number, the actual number. But it's expressed more concisely with scientific notation. How do we read scientific notation if we need to read it out loud? Well, E means times 10 raised to the power of, that's what the E means there. It's not the word exponent, it's not the base of natural logarithms, it's just a way of expressing scientific notation. And so this one would be 2.43 times 10 raised to the power of negative 8. We'll see more about that later. More examples, 999, 888, 7776, that's a large number, but then we're making it even bigger by multiplying it by 8, 8. That extremely large result would be expressed in scientific notation by 8.799, 021243, E11 or plus 11. And again, since it's so many digits and there was really no room for it in the calculator, it's there's rounding, a computer would probably be a better idea here. The second example, we have 0.34 raised to the power of 9 and that's a very small number. We end up with 6.071699277, E to the negative 5, so it's times 10 to the minus 5. And it's a minus sign, so you move the decimal place 5, decimal point 5 places to the left. And you end up with 0.000607, etc. And because of the way things are displayed and because every calculator and every application has a different amount of spaces formatted, it's going to look different in different calculators and in different ways and sometimes they will be rounded. The third example, very quickly, we're going to look at it again, what does it mean? If we see 2.187 and then minus 11 or as you see on the display on the calculator in the image, 2.187 E negative 11, that means it's going to be a very, very tiny number because we're going to move the decimal point to the left 11 spaces. Remember, don't get confused between scientific notation and exponents, exponents can be on any number and it can also be on E, the base of natural algorithms. And scientific notation is always multiplied by 10 and it's powers of 10. The exponent is illustrating powers of 10. Even if it says E, E is just to indicate that we're using scientific notation to collapse a very large or a very small number. The previous example from the previous slide, you see the calculator image there, 2.187 E negative 11, that's the same as it could be displayed as just negative 11 without the E and it's the same as saying 2.187 times 10 to the power of negative 11. And we get 0.000, a lot of zeros and then 2.187. On the other hand, take a look at the two examples following. If we say 3 E minus 2 or 3 scientific notation minus 2, what we mean is 3 times 10 raised to the power of minus 2, which is 0.03, move the decimal point to the left two places. What we don't mean is that the negative 2 is an exponent on the 3, which would be the equivalent to or equal to 1 over 3 squared, which is 1 over 9, which is 0.111. Okay, so not the same. To find more boot camp modules, visit the STAT course at the URL you see there and go to the navigation bar on the left, click boot camp and you'll see all kinds of things that are good to do prior to the statistics course. Many of you have already done this before and maybe only need a refresher.