Welcome to math for electronics, part two. My name is Al and welcome again to Al's electronic classroom. Before we get into this topic again, as I said previously, I'm trying to make this as close to a classroom setting as I possibly can, calling it a virtual classroom. If you have questions, you can contact me through tablet wise. me right there. Or you can give me a call at my numbers 781-202-4396.

I will return calls if you are in the continental United States. So if you do call, I'm not here, leave a message. If you're beyond the continental United States, I still want to help you. Send me an email, we can schedule Call, we can do it through email, we can arrange something, my focus is to help you understand the subjects that I present. With that said, let's clear off the slide and go and get on with our subject. Okay, if you remember from the previous section we talked about the auto replaces.

And we talked about the places from left of the decimal point, going this way. Again, here's my decimal point, right there. I'll just abbreviate it. And what did we know? Well, we as we went to the last we got 10 times greater didn't wait. And this was my way ones, my 10s my hundreds, my thousands.

All right. All right. And we we went through some some examples. We talked about how we display a whole number. All right. And again, if you have questions or you're still uncertain about that, I suggest you go back and review the previous section.

And again, if you have any questions, you have contact information for me. Alright. So now what are we going to do? Well, we're going to talk about, and I'm going to clear the slide here. We're going to talk about the positions to the right of the decimal point, again, is my decimal point. And now we're going to talk about the positions the go To the right.

All right, when we go to the right, we do not get 10 times larger, we get 10 times smaller. All right, and on the next slide, I'll expand this and we'll go into this a little bit deep. So let me clear this slide and we will go to the next one. Okay, here we are on the slide again, we're looking at order of operations is my number line. And again, we're going from the decimal point to the right, and we know we get 10 times smaller. So what are these What are these units or places called?

Well, right here where I have 0.1 Zero dot 010 dot 0010 dot 00010 dot 0001 and zero dot 00001. Now, notice again as I go to the right, what happens? Ah, I insert a zero here. Notice we insert a zero between the decimal point and then next digit or you can think of it this way. I move the decimal point to the left, moving the decimal point to the left decimal point to the left decimal point to the left to the left to the left to the left, right. So by moving the decimal point to the left, I make my number 10 times smaller.

Okay, before we go on, I want to spend a few more minutes on this on this so moving the decimal point and and dividing by 10 or making the number 10 times smaller. So let's just put a number out there. I'm going to start out with one dot zero. All right. Now what did I say if I move my decimal point over to the left, I get, I automatically make it 10 times smaller or decrease the number by 10 times. Well, if I do that, and I move my decimal point this way, what do I have?

And you'll notice how when I have a decimal point, I'll always put a digit to the left of it. So in this example, I'm moving the decimal point again this way. So I do zero dot one, zero. All right, so what have I done? I've moved the decimal point from here. Hear to hear.

So I've, I've divided it by 10. I've made it 10 times smaller. Okay, let's do let's do another one here. All right, let's do zero dot one. And again, I want to make it 10 times smaller. So what do I do?

I move the decimal point, one place to the left. What do I have? Again, I always want to have a digit to the left of the decimal point, which is right here is my decimal point. All right. 01 There it is. All right.

So dot one or zero point One becomes zero dot 01. Let's do one more zero dot 001. I want to make it 10 times smaller so I can move the decimal point one place to the left. So I move my decimal point this way, what do I have? I have zero dot 0001. I have made this number 10 times smaller than this.

So when I move my decimal point When I move my decimal point, one place to the left I divide by 10. When I move my decimal point, one place to the left, I divide by 10. Let's do let's look at this a little bit closer now. And what I'm going to do is I'm going to erase the screen, which I've done there. All right, and Let's, let's put a number up there. Let's just, let's just pick I'm gonna pick a number I had saw, I'm gonna pick a number.

So let's pick a two dot 56. And nothing significant about that number. I just pulled it out of my head. All right, so I want to divide that by 10 or make it 10 times smaller is my decimal point right there. What do I do? I move the decimal point one place to the left.

What do I have zero. dot 256. Okay, notice again, I'm trying to embed this. I always want to see a digit to the left of the decimal point. So I put a zero there. Because there's no value there.

All right, so my new number is 0.256. And there it is, I have decreased or divided the number, this number here divided by 10. already make a little bit more sense. If it doesn't, I keep harping on it. You have a way to contact me through Udemy. And you have a phone number. Give me a call.

All right, let's, let's, let's go on here. And what if I want to make it 100 times smaller and divide by 100? So let's say I want to divide by 100. Well, what do I do? Let's put a number up there. Zero dot Two, three.

All right, so Hi. How many places do you think I want to move? Hey, maybe two, huh? Because as I go to the left as I move my decimal to the left, each time each position, then I move it to the left, I get 10 times smaller. So if I move it two places to the left, I get 100 times smaller. So what would this number be if I want to divide it by 100?

Well, I would move my deadlifts. Well, let's do this. I move my decimal point here. And then here, so let's add a zero because I need to hold the place and a zero is a placeholder. So now what is my new number? Well, I always want to have a digit to the left of the decimal point.

That is my new number. If I divide by 100, or I move my decimal point, two places to the left. All right, let's clear the slide. Let's do one more. And let's see what we're gonna do here. Okay.

So if I move my decimal point, one place to the left, and that equals a division of 10. And if I move my decimal point to place To left I get a division of what 100. So, what happens if I move it? three places? To the left? What happens?

I divided by, and if you're with me, you're gonna say 1000. All right. So every time I move my decimal point, a position to the left or one place to the left, I divide by 10. All right, let's let's clear up the slide. Here. Hi.

And left, I'm going to pick a number. And I want to divide that by 1000. What do I do? How many places do I move it? If you thought of three, you're absolutely right. So I'm going to move this decimal three places to the left because I'm going to move divided by 1000 123.

Don't forget my placeholder, the zero. And of course, I want to have a digit to the left of my decimal point. So in this case, it'll be a zero. So what's my new number? Zero dot zero. 2376 that is my new number.

My original number was 23 dot seven, six, and I divided that by 1000 just by moving the decimal point to the left. All right. All right, let's clear the slide off. One more then we're done. We're going on okay. And I want to divide that by 1000.

What do I do? I move the decimal point. three places to the left 123 my new number. Do I need that zero here? Do I need this zero? No, I don't need it.

It doesn't do anything for me. So this is my new number on I will put some exercises up for you in this section. And again, you have my number if you need a little help. Okay, let's move on. Okay, here we are with our number line and the auto replaces again right there. And we now should know that as we go to the right of the decimal point, I get 10 times smaller.

Or I divide by 10. All right, we know that I've been hammering that and hammering that. So let's clear the slide. Let's, let's look at this a little bit more. So here again, my decimal point. All right.

So we have zero dot one, zero dot 010 dot 0010 dot 00010. Zero dot 00001 and zero dot 00001. And if I went on forever, or the fancy word is infinity, I would keep dividing by 10 or getting 10 times smaller, which means I would move my decimal point to the left. And we did that in the previous section. All right, so what do we call these? Well, let's clear the slide and I'm going to put that up for you too.

Okay, this position right here, is called tense. This position here is called hundredths thousands Thousands, hundred thousands, millions. And then 10 millions 100 millions 1,000,000,010 billion 100 billion 1,000,000,000,010 trillion, and so forth and so on. It keeps multiple billions. I'm sorry, with it. We keep getting 10 times smaller as we go out.

Okay, millions 10 millions 100 millions Remember on putting the th s at the end? billions, and so forth. All right. Um, after a while it gets gets ridiculous, but it never stops. It just keeps on going. Alright.

So if I look at my number line in the order of the places. All right, and again, we're going to stop it. I'm going to review that. Actually, we're not going to do that. Let me just show you one more slide. And then we'll review.

All right, let me clear this off. We're off the slide, go to the next one. And what I've done here is I've made it a little bit nicer for you. Okay, so here's my decimal point right there. And point one a tense point 01 hundred point 001 Point 000 110 thousands, hundred thousands, millions. And again, as I said, 10 millions 100 millions and so forth.

All right. So let's stop here for a minute. I'm going to get another slide up for you. Okay, let's, let's do a problem here. Zero dot 234. And I nothing significant about the number I just pulled it out of my head.

So let's sum. Let's reference that number to the order of places. So what do I have? I have two times zero dot one plus three times zero dot 01 plus four times zero dot zero. 01 so what do we have? Well, two times zero dot one is zero dot two, plus three times zero dot 01 is zero dot 03 plus four times zero dot 001 is zero dot 004.

And when I add them up, what do I get? Well, what we get started out with here, zero dot 234. That's pretty much it. Just what do I got here though, but if I just take this number right here, I've got two tents. 304 thousands. So you can see it's pretty looks very similar to When we spoke about units, 10s, or hundreds of thousands in section one, only now where we're doing the process is the same, only we're looking at items that are less than one, specifically tenths, hundreds, thousands, 10, thousands, millions, and so forth.

And we know as we go to the right, as I move to the right of the decimal point, each place gets 10 times smaller. So let's, let's stop here. Okay, let's, let's do a problem here. What if I give you something like six tenths? Do we know how to write that as a decimal fraction? Sure, we do our tensor right here.

So what do we got? Six times 0.1 equals zero dot six. That's easy. That shouldn't be difficult for you. All right. Let's do another one.

What if I give you six tenths plus? Let's say 200. What would that be? Well, it would be six times 0.1 plus two times zero dot 01. And what would that be? Six, whoops, two.

All right, zero dot six, two. All right. So if we have this chart in front One of us, it's very easy to do, I'm going to clear the slide and give you one to do. I'm going to put some more exercises at the end of this section with the answers you can do them. If you have a problem, you know what to do, you can contact me through Udemy. I've given you a phone number you can call me.

So let's, let's stop here. I'm going to clear the slide and put one or two up up here for you. Okay, how about this one? to tense plus, by thousands, what would that be? Okay, I'm gonna stop it. Give me a minute, and then I'm going to show you the answer.

Okay, here's the answers to 10s plus 5000 is my two tenths my 5000s. Two times 0.1 is zero dot two right here. Five times zero dot 001 is zero dot 005. And when I add them up, I get this. There's the answer. Okay, we're going to stop here.

We're going to go on to the next section. And we're going to talk about addition, subtraction, multiplication and division. Now, this may be a review for some of you, bear with me, we're going to get into the good stuff as we go. So I'm going to stop here and I'll see you on the next section. Again, if you need assistance, email me through this platform. You have a phone number call me.

Talk to you soon see in the next section