All right in this slide here we're talking about multiplication using powers of 10. And some rules, we want to multiply the coefficients and add the exponents. Alright, so let's do one here. So we give you an example. These are straight numbers 200 times 40,000. So we know from the previous section, that when I take when I find the, the powers of 10 of 200, my coefficient is two, and it's 10. raise to the second power right here.

I do the same thing with 40,000. My coefficient is four And times 10 to the fourth power there. So here we go. I'm going to multiply two times 10 squared times four times 10 to the fourth. So what do we say here? I multiply the coefficients.

Two times four is eight, and I add my exponents. Two plus four is six. So there's my answer. Hey 10 to the sixth power. That's it. That's it.

All right. Now let's see what happens when I have negative exponents. All right, again, I'm giving you an example here of zero dot 02 times zero. dot one. So now I'm going to take that zero dot 02. And I'm going to convert it convert it to powers of 10.

And that is two times 10 to the minus two. All right, and then I'm going to take that 0.1. Again, I'm going to convert that to powers of 10. And that's one times 10 to the minus one. And again, if you don't see that, I suggest you go back to the previous lecture here and review negative exponents. So again, all we do, we multiply the coefficients.

Two times one is two, and we add my exponents minus two plus a minus one is a minus three. So here's my answer there. That's my answer. Alright, that's it. Um, again, it's it's really not anything new. We're taking some principles that we, we learned previously.

May it be the last lecture or at the beginning of this course. And we're just applying those rules. All right, and getting a different technique and multiplying numbers. All right. Okay, I'm going to clear the slide and we're going to go to the next one. Okay, on this one here, I've given you six examples.

I really would. It would be beneficial to you, not necessarily to me, but beneficial for you, as a student to stop this presentation and do them. I know I know how to do them. I've been doing them for a while you're taking this course. So you can learn Some of the mathematical techniques, so I suggest you stop the presentation and do them. And as always, when you continue, the answers will be on the next slide.

And I may, I'll may expand upon one or two of them for you. All right, let's stop here. All right here, here are the answers here. I'm going to expand upon one or two of them, maybe three. But if you look at if you're going to look at the first one here, the answer is six times 10 to the sixth. Well, what did we say we multiply the coefficients?

Two times three is six. All right, and I add my exponents. Four plus two is six. So my answer is six times 10 to the sixth. Hi, what's up, let's go over here and do this one here. Seven times.

Tend to seven plus times one times 10. Now I don't have an exponent there, but what is it assumed? If I don't have an exponent assumed to be one, all right? So seven times one is seven, seven plus one over here, even though we don't show it is is eight. So seven times 10 to the eighth. Okay, let's just do one negative exponent.

Let's, let's do this one here. And again, I multiply my coefficients, two times three is six, and I add my negative n exponents minus two, plus a minus four is a minus six. So there's my answer. Six times 10 to the minus six. Okay, we're going to go on to division in the next slide, and again, send me an email. If you look at the beginning of this presentation, as Help number call me again, I do not respond to block numbers.

And I it's very, I do not call back international numbers. So you can get ahold of me via email. If you really need to do something, send me an email, you can't get ahold of me We'll work something out. We'll set up a time or that type of thing. That's beneficial. God, give me a call.

Thanks. All right, now we're talking about divisions using powers of 10. And what we do is we divide the coefficients and then we subtract the exponents. And if you remember, in multiplication, we multiplied the coefficients and added the exponents we're kind of doing the opposite. So I'll give you an example here. 40,000 divided by 200 and as we know, 40,000 is 40. times 10 to the fourth, and 200 is two times 10 squared.

So here we go here. Okay, so we want to divide the coefficients, so four divided by two equals two. Here we are, right there. And what do we do we subtract the exponents. So four minus two equals two. Here we go.

There's my answer. Two times 10 to the second power. All right. All right. Let's look at the bottom one here. I'm going to clear the slide off.

And let's look at the bottom one here where we're using negative exponents everything's the same, we're going to divide the coefficients and subtract the exponents. So zero dot zero to converts in powers of 10 is two times 10 to the minus two, and zero dot one converts to one times 10 to the minus one right there. So again, we divide the coefficients, so two divided by one equals two, right there, and now minus two right here, minus a minus one. Well, what happens? we now get Don't forget, we're subtracting a negative number, minus two minus a minus one becomes a plus one. And that equals A minus one right there though.

That's my answer. Right here. All right. All right. Let's stop and go on to the next slide night and I give you some examples for you to do. All right, here are some examples I'd like you to do.

Just remember down here, this one. Actually, these three right here, you've got some negative exponents. All right, so you may or may not have to do something with the sign. You may need to change something with the sign on these two here. I so pause the presentation, do them. And as always, the answers are on the next slide.

And again, you have a phone number. You have an email. I'm here to help. Okay. Here are the answers. And if you notice here in here, we had to change the sign there on those exponents because we were subtracting a negative number.

All right? And that's why this became 14. And this became positive too. All right. All right, any questions, give me a call, and or send me an email, and we'll help you out. Talk to you soon.

We've got one more section to go on this part here, I should say one more lecture on this section. And then we're off to a log and logarithms. All right, seeing the last lecture on this section.