 This video is going to talk about scientific notation. There are a couple of things that we need to know about scientific notation before we can actually work with it. So here's the basics. N is some number, and it's going to be times 10 to some exponent. And the number of N has to be between 1 and 10. It can be 1, but it cannot be 10. It has to have one digit in front of that decimal. So the exponent K is going to be an integer, so it's either going to be a positive number or a negative number. If it's a positive K, it means that the number that we're working with was greater than 1. And if it's a negative K, that means that our number is less than 1. So let's go from standard form to scientific notation. If you look at these first examples, we all know that the decimal in this number is actually behind the 0. 250, it would be 0.0 if we wanted to put it something behind the decimal. But we need to move our number so that it is a number between 1 and 10. If I move it to in front of the 0, I have 25, and that's greater than 10. But if I move it between the 2 and the 5, I have 2.5, which is between 1 and 10. So I write 2.5. And then how many decimal places I moved is going to be my exponent. So we moved two places, and it was a number larger than 1, so it's a positive 2 exponent. Over here in this example, you can see our decimal here. And if I move my decimal one place, it's going to be still a number that's smaller than 1. It would be 0.25. If I move it one more place, now I have 2.5, which is between 0 and 1. So I write my 2.5 times 10, and then this number was less than 1. So that means that we have a negative k. And we moved it two places, so it's going to be a negative 2. So let's try some examples. First of all, this number is less than 1. That means that my exponent over here is going to have a negative on it. So we have to move our decimal. If we move it one place, now we're going to be at 1.234, and that number is between 1 and 10. If I went one more, I'd have 12.34, and that's too big. So remember, you only have one digit in front of the decimal, so it's 1.234. We still have to write all those numbers. And we moved it only one place, so it's to the negative 1. Now I have a number here that's greater than 1, so that means that my k is going to end up being positive. So we'll have a positive exponent over here. And remember, the decimal's behind the last digit if we don't see the decimal. So we go 1 and that's 7,000 plus, and I go 2 and that's 700 something. 3 will give me 73, and if I move it four places, now I'm at 7.3. So my one digit in front of my decimal is 7, and then 3, 9, 2. And we said we moved it four places, so it's 10 to the fourth. Now let's go from scientific to standard form. Again, let's look at a real example. We have this number 1.88, and then it says times 10 to the negative 3. So this means that our number is going to be less than 1 because we have this negative exponent. To make this number less than 1, I'm going to have to move it to the left. Move it one place that gets me in front of the 1, and then I'm supposed to move it two more places. I have to fill those spaces with zeros. So I have .00, there's the two spaces I had to fill in, 1, 8, 8. So 1.88 times 10 to the negative 3 is .00188. We look at this example. We have to move it six places, and we know that this number is going to become a very large number because it's bigger than 1 because of this positive 6 here. So we have to move our decimal to the right. So 4.5, I'm going to move it to the right. 1, 2, 3 gets me behind my number, but I still need three places more. 1, 2, 3, so here's the three places that I had to add. I'm going to put zeros in for that. And then my 7, 6, 5 work your way backward 4. 4.567 times 10 to the sixth is 4,567,000. Alright, now we have to try it without seeing the answer. Look at the K. K is positive, so that means that my number is going to be greater than 1. So I have to move it to the right to make my number bigger. And I move 1, 2, 3, I'm behind my number, and then I have to add one more to make four decimal places. 8, 0, 2, 5, and then one more zero. 80,250. 1.11 times 10 to the negative 5. I look at this exponent, and that tells me that K is a negative. So I know my number is going to be less than 1, which means I have to move to the left. That'll move me here. And so I move one place in front of my decimal, but I still have four more to go, so I'm going to have to add four zeros on the front. Point, and then 1, 2, 3, 4 zeros, and then 1, 1, 1. So if I want to check these just to make sure that I did them right, look at this one, 1.88 times 10 to the negative 3. We know what the answer is going to be, but let's just double check that with our calculator. So it's a 1.88, and then there's two options here. You could do second log. The log key's over here next to your 7, and that's your times 10, and you just have to put your exponent in there, so negative, and make sure you use a negative key, 3, and then close your parentheses, and that will give me my answer of .00188. So we knew we did that right. We do the second example down here just to double check. We put in our decimal, 8.025, and then the other option is to say second, and then comma, and that E just means I'm going to put the exponent of scientific notation. That means scientific notation, and my exponent was 4, and I can just press enter. Get 80,250 just like we did when we were doing it by hand. If we wanted to check these type of problems, we could also do that by saying, putting in what we thought our scientific notation should be, and then checking to make sure that it gave us the right number. So let's check this one here. We have 1.234, and I prefer, I don't know why, but I prefer second comma, so that's what I'm going to do. So there's my 10 to the whatever. It's not as obvious that it's 10, but all I have to do is put in my negative 1, and I don't have to worry about the parenthesis. I think that's why I like it. Press enter, and it's 0.1234, and that's exactly what we started with, so I must have done my scientific notation right.