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There are two whole Khan Academy videos on what scientific notation is, why we even worry about it. And it also goes through a few examples. And what I want to do in this video is just use a ck12.org Algebra I book to do some more scientific notation examples. So let's take some things that are written in scientific notation. Just as a reminder, scientific notation is useful because it allows us to write really large, or tiny numbers, in ways that are easy for our brains to, one, write down, and two, understand. So let's write down some numbers. So let's say I have 3.102 times 10 to the second. And I want to write it as just a numerical value. It's in scientific notation already. It's written as a product with a power of 10. So how do I write this? It's just a numeral. Well, there's a slow way and the fast way. The slow way is to say, well, this is the same thing as 3.102 times 100, which means if you multiplied 3.102 times 100, it'll be 3, 1, 0, 2, with two 0's behind it. And then we have 1, 2, 3 numbers behind the decimal point, and that'd be the right answer. This is equal to 310.2. Now, a faster way to do this is just to say, well, look, right now I have only the 3 in front of the decimal point. When I take something times 10 to the second power, I'm essentially shifting the decimal point 2 to the right. So 3.102 times 10 to the second power is the same thing as-- if I shift the decimal point 1, and then 2, because this is 10 to the second power-- it's same thing as 310.2. So this might be a faster way of doing it. Every time you multiply it by 10, you shift the decimal to the right by 1. Let's do another example. Let's say I had 7.4 times 10 to the fourth. Well, let's just do this the fast way. Let's shift the decimal 4 to the right. So 7.4 times 10 to the fourth. Times 10 to the 1, you're going to get 74. Then times 10 to the second, you're going to get 740. We're going to have to add a 0 there, because we have to shift the decimal again. 10 to the third, you're going to have 7,400. And then 10 to the fourth, you're going to have 74,000. Notice, I just took this decimal and went 1, 2, 3, 4 spaces. So this is equal to 74,000. And when I had 74, and I had to shift the decimal 1 more to the right, I had to throw in a 0 here. I'm multiplying it by 10. Another way to think about it is, I need 10 spaces between the leading digit and the decimal. So right here, I only have 1 space. I'll need 4 spaces, So, 1, 2, 3, 4. Let's do a few more examples, because I think the more examples, the more you'll get what's going on. So I have 1.75 times 10 to the negative 3. This is in scientific notation, and I want to just write the numerical value of this. So when you take something to the negative times 10 to the negative power, you shift the decimal to the left. So this is 1.75. So if you do, it times 10 to the negative 1 power, you'll go 1 to the left. But if you do time 10 to the negative 2 power, you'll go 2 to the left. And you'd have to put a 0 here....
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