Okay, here we talking about the metric system. And the metric units I use both in scientific and in the engineering world. And here are my prefixes right here. And when I'm going to mention the correct pronounce, not the correct but the way they're pronounced ciated or pronounced I should say. So the first is Giga, mega, kilo, milli, micro, nano and Pico Chi. So, I mean, that's how you'll hear them.

All right. Now, if you remember when we spoke a while when we looked at powers of 10. And we mentioned that in the engineering world. We want to have Are when we solve the problem our units in multiples of three, we'll have you look at my exponents here. You'll see they're multiples of three. So I got 963, then minus three minus six minus nine, and minus 12.

There. All right, so those are in multiples of three. All right? We give you some examples that again, we're looking at the engineering technical world with this. So four gigahertz, right Giga, G, right there is four times 10 to the nine. So instead of saying four times 10, to the nine hertz, we say, four gigahertz, okay?

An example would be two mega ohms right there, okay. ohms is the measurement of resistance measure. means 2 million. So if I look at powers of 10, right there on on, on this one, it would be two times 10 to the sixth 12 kilovolts. All right, that's 12 times 10 to three volts. All right, those right from here up are units that are greater than one.

Now down here, we've got units that are less than one and milli 50 milliamp hours, okay, that's 15 times 10 to the minus three micro seven micro ampere is right there. Okay, and that's seven times 10 to the minus six 100 nanoseconds, that's 100 times 10 to the minus nine and 20 pico farad, which is actually is a measurement of capacity. That's 120 times 10 to the minus as well. So right now on this slide, the only thing we're doing is we're introducing you to the prefixes in the metric system. We give you the prefix nine over here, as you may hear them or as they're supposed to be communic verbally communicated the equivalent powers of 10 and some examples. Okay, so let's stop here and go to the next slide.

Okay, and this slide here, what we want to do is we want to convert the following to a metric prefix, so Giga as Giga powers 10 to the nine and so forth up here. All right. So 10 to the ninth is Giga, right? So four gigahertz is actually 10 times four times 10 to the nine hertz. All right. So What we have to do is find the power of 10 to the prefix.

So another example would be 10 times 10 to the sixth. Six is mega, right there. So 10 times 10 to the six ohms is 10 mega ohms, which I show you right there. All right. So we find the equivalent prefix that corresponds to the power of 10. Again 10 to the sixth is mega.

Now, let me ask you something, if I had something that was one times 10 to the minus nine, that would be nano. All right. And if I had something was 10 to the minus six, it would be micro, and 10 to the minus three would be milling. Alright. Okay. So again, powers of 10 and multiples of truth three, find the corresponding metric system prefix.

Okay in this section here on this slide here, what I want you to do is convert to a metric prefix or convert to powers of 10. Okay, so, I'm gonna do the first one for you. So what do we got? We got 0009 amps. All right, so what, what I want to do is, I want to get a power of 10. That's in multiples of three So that would be milli, wouldn't it because if I move the decimal point three places, I get nine milliamps I, that's kind of nice.

Now, if I moved over another three, that would be 900 micro amperes. Right there, right? And I'd add three more zeros. Then I could add three more zeros right here and get 900,000 nano amps. That's just isn't, isn't right. So, we're going to stick with nine milliamp hours, because we kind of want this number here, which we call the coefficient to be around one if we can or the lowest number that we can get.

Okay? So nine is good. So what I'd like you to do is do these two 5 million ohms are zero dot 000006 seconds. All right, so you're going to give me the prefix on that. And over here, I'm going to do this first one to you. 47 Pico, Pico farads.

And that's right here. And what is that? That's 10 to the minus 12. So what would this be? This would be 47 times 10 to the minus 12. Ferrets, that's that's what that would be.

All right, see if you can do the other two, the other four, two on each side. And we'll give you the answers on the next side. I apologize about the the writing here but Okay, here are the answers. We did these two in the previous slide. So let's let's look at this. One we've got 5 million ohms.

How many zeros 12345 610 to the six mega five mega ohms is my answer right there. All right, we've got point 0.000006. How many decimal places do I have to make to make that number whole 123456 minus six. So it's six micro seconds. All right. Over here, we're going from we're converting to power.

10 So I've got four megahertz, mega is 10 to the minus 610 to the plus six, so I got four times 10 to the six hertz. Over here, I have six microseconds. Micro is 10 to the minus six. So I have six times 10 to the minus six seconds. That's it. So all we're doing here is either assigning a metric prefix, or in this exercise, we've given you a metric prefix.

And we want to know what is the equivalent powers of 10. All right, stop here and and go to the next slide. Okay, on this slide here, we're going to talk about powers of 10. And when powers of 10 don't match the metric system prefix, okay, if you remember from the previous slide, okay, we wanted to go in multiples of three, because we had milli micro nano Pico kilo mega, okay, they were all multiples of three. But then again, if we don't have multiples of three we what we have to do is we have to change the power of 10. Okay, so we get either 369 12 minus three minus six minus nine minus 12.

Okay and then we can match the metric pre prefix up with that with that particular power of 10. So, to do that, we need to adjust the coefficient If you remember that part of the power of 10 number is the coefficient. And then when we move on decimal one way or the other with our coefficient, and we adjust our exponent on our power of 10. All right, so let's clear the screen off and let's do the first example. Right here. Okay, and let's look at that this first bullet rule here.

Okay, move the decimal on the coefficient to the left, and then increase the exponent by one for each position. Okay, so what do we want to do here? Well, if you look, we've got 10 squared. We want to make that multiples of three. So hey, how about Increasing that to 10 to the third. So if I do that is my decimal point right there.

So I want to go to 10 to the third. So I have to move the decimal on the coefficient to the lap. All right, so I'm going to move it here, like I show you there, right? And I get seven dot zero and I increase my exponent by one and notice I go from two to three. So my answer here is seven times 10 to the third. If you remember when we talked about metric prefixes, 10 to the third is kilo.

So I have Seven kilo or seven k all on that example. All right. Okay, let's look at the bottom one now. All right. And notice we've got 10 to the four here. All right?

So let's look at this, this rule here, the second bullet point, it says move the decimal on the coefficient to the right. And then I decrease the exponent by one for each position. Well, I've got 10 to the four here, don't I? And I want what multiples are three. So I move my decimal point one place to the left over there, and I decrease my powers of 10. So my answer is at times 10 to the third.

And again 10 to the third is kilo. So my answer is 80 K or 80 K. kilo ohms, which is a measurement of resistance. All right. So there we have it. All right, I suggest you kind of remember these here, because we are going to give you a couple of examples to do later on. But the other point I want to make out here is, it may look like it's it's a difficult thing here.

But quite honestly, after you do a couple, and you're in the trade and you've done them for a while, you don't even have to think about it. You just kind of move the decimal and say, Hey, this is milliamps. This is micro amps. This is k ohms. This is mega ohms. Really, it looks it may look a little bit intimidating, but after you do a couple, it'll get really easy.

And I mean that Okay, let's stop here. Okay, now we're talking, we're doing the same thing or we're talking about Same thing, but this is what we do when we have negative exponents, okay, meaning my powers of 10 are less than one. Okay, so let's look at the first bullet here. And when I move the decimal on the coefficient to the left, I decrease the exponent by one for each position. So we've got right here on this example, we've got nine times 10 to the minus four amps. Okay, we want to move the decimal one position to the left, because we want to decrease the powers of 10 by three.

All right, so when I move my decimal point to the left, I decrease the exponent by one. So you'll notice I went from minus four to minus three So therefore my answer is nine times 10 to the minus three and if you remember from our discussion again, on matrix system prefixes minus three is milli. So I have 09 milliamp hours right here. That's my answer. All right. Okay, let's, let's look at one more here, I'm going to race the slide.

Now on this bottom example, notice that we have minus two. And we want to go to minus three again, because that's milliamp hour, but up here, we will negative four, down here, one minus two. So I have nine times 10 to the minus two power amps. So I want to increase The exponent by one. So I move the decimal point on the coefficient to the right by one place. So notice I go from nine to 90.

So I've got 90 times 10 to the minus three, which equals $90 million, which somehow I missed that right there. I'll fix that on the slide. So it's 90 milliamp hours is my answer there. Okay. All right. Let's go on to the next slide.

All right, here's some problems with some examples you can do, I've given you six of them down here and I've actually given you a hint, milliamp ers, so change that this to milliamp ers micro amp is mega milliamp hours micro amperes coulombs. One thing I want to want to mention, notice we've got four positive rules for positive exponents and rules for negative exponents. If you'll look, you'll see that these are reversed. Now the words their opposite. So, positive exponents when I move the decimal on the coefficient to the left I increase. When I move the decimal on the coffee to the left, I decrease so they're reversed.

And when I'm right here, when I move the decimal on the coefficient to the right I increase when I move the decimal coefficient on the right I decrease. So these two and these two are as far as if I increment or decrement. The coefficient on the powers of 10 is is is opposite. Just wanted to point that out. Take a look at it. If you go over these, you'll see what I'm, what I'm what I mean by that by reading that.

Okay? So with that, try to do those stop try to do them. And, as always, the answers are on the next slide. Okay, here are the answers for the from the previous slide. What did we do here? Okay, we originally we had seven times 10 to the minus four, we decreased a negative power of 10 by one.

So again, move the decimal on the coefficient to the left when I decrease the exponent by one for each position. So I went from minus four to minus three, I decreased it, all right, and so therefore I move the decimal one place to the left which I've done that okay. So I've got a point seven times 10 to the minus three $0.7 million. Okay, over here, this one here, what did I do? I increased my power of my negative power of 10. Right?

So when I increase the exponent by one, I move the decimal on the coefficient, right, which I've done here. So I go from 19 to 190. And this one here, this is positive, positive power of 10. I go from five to six. All right, so I move right here. We're doing this one.

So I move the decimal on the coefficient to the left right here. 2.2 right there. So I get 2.2 times 10 to the six. So I got 22 mega ohms. Okay, you can look at these on your own right there should be pretty much self explanatory. And it happens have any questions?

Give me a call, send me an email on this platform I will assist you. Alright, let's stop here.