00:02 Hello, my name is Sunday Oyase.

00:16 I will be taking you Mat Matis, the GSS2 class,

00:18 and we have an interesting topic for today.

00:21 The topic of today is O Numbers.

00:24 Well, the O Numbers have,

00:26 I will be dividing into two series.

00:28 We'll be looking at it from two series

00:29 because it's a whole lot of activities for the O Numbers.

00:32 So, we'll be looking at the first part and the second part.

00:37 But this up class is dedicated for the first part

00:40 of the O Numbers.

00:42 What is the objective of the class?

00:46 The objective of the class is to express any O Numbers

00:50 in standard forms.

00:51 Now, when you see an O Number,

00:54 how do you express an O Number in standard form?

00:57 Become the first objective of the class.

00:59 So, definitely we have to know what is whole Numbers.

01:01 We have to know what is standard form

01:03 and know how to express them in standard forms.

01:06 That we'll be expressing decimal number in standard form.

01:11 So, expression of Numbers in standard form,

01:14 expressing decimals in standard form,

01:16 and we'll be finding the fine factors of Numbers that are

01:20 greater than 100, not greater than 100.

01:23 Now, the objective is simply to look at standard forms,

01:28 decimal numbers, and prime factors.

01:31 Okay, so, we move on.

01:34 What are all Numbers?

01:35 It becomes so important.

01:37 What are all Numbers?

01:38 Our all Numbers are the numbers starting from zero

01:42 and counting all forever.

01:44 We call that all Numbers.

01:46 We start from zero to forever.

01:48 So, we have, if I have the all Numbers,

01:53 I'm counting from zero, one, two, two, infinity.

02:00 I call that and whole Numbers.

02:05 So, it becomes so easy for me to know.

02:08 Now, but when you look at it,

02:10 all Numbers do not include negative Numbers.

02:13 You know, the side of the graph is already divided into two.

02:15 So, if you look at it, we always have our graph in this form.

02:19 You have your graph in this form,

02:22 where you have two sides.

02:24 We have, from here, we have the negatives,

02:27 come, the negative Numbers come in this form.

02:31 Then this side is the positive.

02:33 So, we can say, one, two, three, four,

02:39 forever, then we can have as yes,

02:42 minus one, minus two, minus three, minus four.

02:46 So, from this is point zero, this upward.

02:51 So, all Numbers do not include negative Numbers.

02:56 So, as such, it means that all Numbers do not include

03:00 negative Numbers, not include fractions or decimals.

03:03 So, you could see the range.

03:04 We say all Numbers, so, we could just say,

03:07 all Numbers are positive Numbers.

03:08 So, we have, from zero, down to infinity.

03:13 So, now we continue.

03:16 What are integers?

03:17 Now, integers are like all Numbers.

03:20 They are like all Numbers, but they include negative Numbers.

03:23 So, what are the difference between the all Numbers

03:25 and integers?

03:26 The integers, the difference in the tiny line

03:28 between the integers and the all Numbers,

03:30 is that the integers can take in the negatives

03:34 and also the positives.

03:36 So, we have integers, but still,

03:39 no fraction is allowed in integers.

03:41 So, if I have, I have minus three,

03:45 minus two, comma one, five, eight, nine.

03:50 I have a, so this becomes an integer.

03:57 You call this an integer, why?

03:58 Because it includes a negative and the positive,

04:01 but not an all Numbers.

04:03 So, I have one minus one, minus two,

04:06 minus three, like you have,

04:08 you have where I'm gonna stand, to positive 10.

04:11 So, we're starting the range from minus 10

04:13 to positive Numbers, or 10.

04:16 So, categorically, you will see that these are integers.

04:21 Let's move to the second category now, main category,

04:25 or we're talking about today with the standard forms.

04:28 Now, we say that the integers,

04:31 we talked about the all Numbers.

04:33 The all Numbers are Numbers that are expressing positions.

04:37 The integers are Numbers that are expressing

04:39 both positive and negative form.

04:42 So, you have the combination of the two

04:44 to give you your integer.

04:46 Now, how do we not express this number?

04:48 It's what we refer to as what?

04:50 Our standard form, too.

04:52 Repeat standard form.

04:54 Standard form is in standard form,

04:56 in Numbers within, in the form of A,

04:59 multiplied by 10, which is to power N.

05:01 So, I have my standard form,

05:04 my standard form,

05:09 are Numbers that are expressed in A,

05:12 multiplied by 10, which is to power N.

05:16 The N now could just be the all Numbers.

05:21 And also, the N can also be integers,

05:23 as it could also be all Numbers and negative Numbers.

05:26 So, the general form, we said an A,

05:29 number one, or good time of 2010.

05:32 So, we have positive integers.

05:35 So, we could, now, how do you not express

05:39 your standard form in whole number and in decimal?

05:42 It becomes very important.

05:44 That becomes an issue that we need to look about.

05:47 Now, let's look at this example one.

05:49 We have example one.

05:53 Let's say is express, express, express,

06:02 9, 0, 0, 0, 0, 0, 0, 0.

06:09 Instandard forms, 9, 0, 0, 0, 0, 0.

06:13 Instandard form, before.

06:15 Now, take a look at it.

06:17 I said in the solution, the first thing is the forward movement.

06:21 From the first digit, look at the forward,

06:24 you take the forward movement and it has to be negative.

06:28 So, let's move ahead.

06:30 Now, it's positive plus multiplication.

06:33 So, let's take forward movement.

06:35 We start from the last value, move it forward.

06:38 How many points?

06:39 We say a one, a two, a three, four, five, six, seven.

06:44 The movement comes seven.

06:51 So, we move from the first digit,

06:53 one, two, three, four, five, six, seven.

06:59 Until you get larger.

07:01 So, I could just say, nine multiplied by,

07:05 how many times did we move the movement?

07:09 Let's say forward movement.

07:10 How many times will we move it multiplied by seven?

07:14 So, we have one, two, three.

07:16 We have one, two, three, four, five, six, seven.

07:18 We have seven.

07:22 So, now, looking to it, it means that each of them

07:27 can be represented in tens.

07:29 Each of the zeros can be represented in tens.

07:32 So, when we want to represent the zeros in ten,

07:35 now, put it in tens.

07:36 We have nine multiplied by ten, multiplied by another ten.

07:41 Multiply by another ten.

07:45 That's one, two, three.

07:46 Multiply by another ten.

07:48 One, two, three, four, five, six, and seven.

07:53 So, I have seven.

07:58 Now, it means that I could just simply say

08:01 that this is 10, super one, super two,

08:04 super one, one, one, one, one, one, one, one, one.

08:07 So, how many number of tens do we have?

08:09 We have seven.

08:10 So, expressing these, I will simply say 10,

08:14 nine times 10 raise to power seven

08:17 because I have how many tens?

08:20 Seven.

08:21 Now, whatever I don't have expressed the number,

08:26 which is 90 million in standard form.

08:31 So, and I have nine times 10 raise to power seven,

08:35 mean that 10 is expressed in seven places, seven places.

08:40 So, when I multiply it back,

08:43 I could always get back my answer.

08:46 Now, also have another example, two.

08:50 Now, looking to example, two, like I said,

08:52 forward movement.

08:53 Have that in mind that the movement is not decimal.

08:58 If it is expressing all numbers,

09:01 the movement is always, always worth the forward movement,

09:04 the forward movement.

09:05 And every forward movement is positive.

09:08 So, now, moving forward, forward movement from what we have.

09:13 So, I have example two.

09:18 Now, my example two says, I have six,

09:24 six, how many zero do I have?

09:27 One, two, three, one, two, three,

09:29 one, two, three, one, two, three, one, two.

09:32 I mean, I have 12 zeros, three, three,

09:35 another three, another three, and another three.

09:40 And another three.

09:41 So, I want to three, one, two, three, six, seven, eight,

09:44 nine, 10, 11, I have 12, 12 zeros now in standard form.

09:49 Like I said, forward movement,

09:51 I keep up the forward movement.

09:53 So, you pick from the large digit,

09:55 you take a forward movement.

09:56 So, let's take the movement.

09:58 We have a one, a two, three, four, five, six,

10:03 seven, eight, nine, 10, 11, 12.

10:11 So, easy to do.

10:16 Now, it means that you move, okay?

10:18 Move up, one, two, three, one, two, three.

10:23 That's six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18.

10:28 Oh, we have 18, not 12.

10:31 So, look to it, 18, not 12.

10:35 So, let's pick 18 form.

10:37 So, I have one, two, three, okay?

10:42 One, two, three, and 18 form.

10:46 I have one, two, three, one, two, three.

10:51 One, two, three.

10:54 That's nine, one, two, three.

10:58 That's 12, 13, 14, 15, 16, 17, 18, okay.

11:03 Now, like I said, forward movement.

11:08 So, let's move it forward, forward movement.

11:10 I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

11:24 Now, hopefully, well, I have 6 multiplied by 10 into 18 to time 10, time 10, time 10, time

11:35 10, time 10, into 18. That's to complete 18. So, I will just simply have it to be 6 times

11:49 10 ways to power how many times they move it 18. Now, why am I not putting the negative

11:55 is because it's a forward movement, a transpositive. But by the time we're looking at further more

12:01 examples, we have, look at example 3. It becomes a different ball game, for example, 1 and

12:09 example 2. Now, example 3 is now expressing numbers, decimal numbers in standard forms.

12:16 Example 3. Now, expressing decimal numbers in standard forms. This now involves what

12:24 we refer to as what we call the forward map. Now, look at 3, 4, 2, 5, 0.1, 0.8, 9, in

12:34 standard form. Now, see, this is decimal. And as far because it is decimal, we also move

12:40 it in forward movement. So, example 3. So, I have 3, 4, 2, 5, 3, 4, 2, 5, 6, 0.1, 8, 9.

12:57 Now, we say forward movement. So, let's move it forward till we get to the last digits. So,

13:02 move will have 1, 2, 3, 4. How many points? 4. So, the point moves to forward. So, I will now have

13:13 what do I have? When the point moves forward, I will have 3 points. Look at that. 4, 2, 5, 6, 1, 8, 9,

13:26 multiply by how many times do the point move? 1, 2, 3, 4. Then I have 1, 2, 3, 4. So, categorically,

13:37 I could just say 3. 4, 2, 5, 6, 1, 8, 9. Multiply by 10 in how many places? 4, 2, 3, 4. So,

13:53 expressing how I have 3 points, 4, 2, 5, 6, 1, 8, 9. Multiply by 10 in how many I will have 4.

14:04 That becomes so easy. It becomes so easy. What I want to do is to be able to flex around with it,

14:11 flex around with how you go about the forward movement. Now, there would be look at example 4.

14:21 Now, we are going the backward movement. Because forward, there are no digits. So, there are digits

14:28 backward. And so, because there are digits backward, we move backward. And for every backward movement,

14:34 a backward movement is a negative movement and also a division movement. So, moving backward,

14:42 from example 4, we move backward. Let's move backward a bit. Now, we have example 4.

14:49 So, I have 0.0. How many zeros? 1, 2, 3, 4, 5, 2, 3, 4, 5, 7. We're moving backward. So,

15:03 it's not multiplication as usual. It's going to be division. Because the movement is not what

15:08 backward. Take note. If the movement is forward is multiplication. If the movement is backward is

15:14 division. So, let's take note. Move. 1, 2, 3, 4, 5. You have to move to the back. 7, 6. Again,

15:28 1, 2, 3, 4, 5, 6. How many zeros do I have? I have 6 zeros. OK? 1, 2, 3, 4, 5. Then 6.

15:39 Now, so, I have 6 points comes here. Now, it means that what this implies is

15:51 7 divided by how many? 1, 2, 3, 4, 5, 5. 1, 2, 3, 4, 5 plus the 1, make it 6.

16:03 I mean this divide by this. So, what do I need to have here? If you look at it carefully,

16:08 what have I just done? It means that since the movement is backward, it becomes a division.

16:12 And so, what am I going to be having? I'm going to be having this. Having 1, 2, 3, 4, 5 plus

16:19 the 1, make it 6. Now, what? Why are you doing this? Because you're moving the point backward. If

16:25 it is backward, it's a division. Forward is multiplication. So, now, being backward, we could just

16:32 easily have it as 7 over this give us 10 times how many forms? 1, 2, 3, 4, 5, 6 times 10

16:45 into 6 forms. 2, 3, 4, 5, 6. So, I have 1, 2, 3, 4, 5, 6. So, look at it. 1, 2, 3, 4, 5. Why? Because

17:03 it is division. We moved backward. That's out of a 7. So, if you look carefully, so we have,

17:10 what do I have? I have 7, 7 over how many times do I have? I have 10 ways to power 6.

17:20 Because of the sign of division, because I'm into this sign of division, I would not have it as 7,

17:27 divided by 10 ways to power 6 in this form. Now, if you look at this form, this is

17:37 equivalent to this. Look at it carefully. This is equivalent to this. But, I need to make this

17:44 to be multiplication, because this cannot be my answer. I need to convert this to multiplication,

17:50 and how do I do that? Now, this is 1 over, okay? 1 divided by this. I need to convert this into

17:59 multiplication. How do I do that? That's the first question. How do I do that? That this one is bit,

18:06 how do I do that? It becomes a question. That's how it's supposed to be. So, how do I make this

18:11 possible? You make this possible by making this up, taking this down. And once you do that,

18:17 this sign changes. So, I have divided by 1 over 10 ways to power 6. If you make this multiplication,

18:25 this moves up, this moves down. So, I'm going to have it as 7 times 10 ways to power minus 6. Because

18:36 this is moving up, it becomes a minus. That's negativity. Take notes. It becomes very important.

18:43 It becomes very important. Now, looking at it again, another example that we have in the part of

18:50 division. So, you could have a profound understanding of what we're doing as example 5, which is

18:56 very important. Example 5. So, we could just, because we have a good knowledge of it,

19:02 we could move it up. So, I have how many points am I moving? I have zero points. How many is there?

19:07 1, 2, 3, 4, 5, 6. Now, if we look carefully, we now have our finer answer as

19:14 as 7 multiplied by 10 ways to power minus 6. Now, 10 ways to power minus 6. So, with this, you have

19:23 an idea that the movement is backward. The backward movement, it becomes an easy to go around it.

19:31 Once the backward movement, a forward movement, positive, a backward movement, negative.

19:36 Now, let's take the other expression. That express standard form. Express standard form in

19:42 ordinary form. So, you take it from the standard form and put it into ordinary form. Before we

19:48 take it from the ordinary form into standard form. So, you could also take it from the standard form

19:52 into an ordinary form. So, we pick an example that we have on the board. We have an example that

20:01 says 7 as an example. We have 7.872 multiplied by 10 ways to power 5.

20:14 Now, this is in standard forms already. I will expect it to take it from standard forms

20:22 to the ordinary form. But what do I say? 10 ways to power 5 means 10 express in 5 places.

20:28 Now, take it off. So, we're going to be having 7.872 multiplied by 10 in 5 places times 10 times 10,

20:42 1, 2, 3, 4, 5. Now, which gives us 7.872 times 10, 1, 2, 3, 4, 5. Now, if you look at it carefully,

20:59 what do we do? If you want to move your point, there's a logic around it.

21:04 You know, now you're moving your point back. So, you're taking it from another form. So,

21:07 let's move it up. If I move my point here, I'll take 1, 2, 3. So, I'm taking the first 3, 0, off.

21:15 Then, I will have this 3, 0s. I've gone for this to move the point to the back. Then, I have my last

21:22 2, 0s. I'll have it to it. So, I will just simply have 7, 8, 7, 2, add my last 2, 0, 0, 0. Simple.

21:32 It becomes an easy to go around. It makes the work very easy for you to do.

21:39 Now, with this, you will have to flex around. Remember, the movement of your point, the movement of

21:44 your point becomes very important. Now, there's an aspect to clearly look at. The aspect that

21:50 is called the prime factorization. Now, what are the prime factorization has to do? Remember,

21:56 from our objective, we said we're going to be looking at the prime factors of less than 100. So,

22:01 let's look at the prime factors. prime factors of the number are the factors of that number,

22:06 which are not divided divisible by any other number except by the number and the cell.

22:12 No other number can divide this number except the number and each cell that can divide the cell.

22:18 So, what are the prime factors around 100? Look at them. The prime factors around 100 are,

22:25 from the table we have two, we have five, we have seven, I have eleven, I have thirteen, seventeen,

22:37 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and finally, 97.

22:58 Now, but the question is, let's pick a question and how do we not express it in this form? Like we've

23:05 done. It turns to power n, it's already expressing in this form. So, if I have three rest to power two,

23:15 this simply means three times three. So, it means that I'm expressing this three in two forms.

23:22 So, in this form, simply means indent form that makes the work easier. So, let's take one example.

23:30 I said express 22 in its factor, prime factors, poor dot of its prime factors. Let's start with

23:38 example one. I said express 22 in its prime, it is factor form. One, prime factor, two, and poor dot

23:49 of its prime factor three. Express 22. So, we take off. We are expressing 22, or the prime

24:01 factors of 22. Numbers that can divide 22 without remainder. One, factors, possible factors of 22,

24:09 what numbers can divide again from R, from R table? Remember a table. Technut of your table,

24:15 we have what are the factors? We have two, two divide 22. That gives 11. So, 11 also can also go

24:25 and 22, the number itself. Now, these are called the factors of 22. They are the factors of 22.

24:33 But the question is what are now the prime factors? The prime factors. Remember from your indent,

24:40 one is not there. So, one is out of the equation. So, the prime factors of 22. The prime factors

24:48 of 22, these are the prime factors. We have two and 11. Technut. Those are the prime factors.

24:59 Now, what would not be the poor dot of the prime factors? Remember a question taking three.

25:04 What would not be the poor dot of prime factors? Poor dot of prime factors. See, the prime

25:11 factors already two and two and 11. Poor dot of the prime factors would not be the multiplication of

25:18 the two. That would be two times 11. And that gives us what? 22. Now, looking at it very well,

25:27 it becomes so simple. All you need to work with is work around the table and you will be able to

25:32 have some other ideas on what are possible prime factors. How do you look at the prime factors?

25:40 So, that becomes an easy example for you to come across. Remember you need to get your

25:48 factors of the numbers. You need to get your prime factors from the table given and you multiply

25:56 the poor dot of the prime factors. Now, their evaluation, their questions we expect you to be

26:02 able to do. And these questions will give you an idea on how you express in standard form.

26:08 So, express the following in standard form. Zero point, zero, zero, zero, zero, zero. That's five

26:14 zeros, that's five, zero, one. Zero point, three, zero, zero, nine, three, nine, three. Zero point,

26:22 three, zero, zero, five, five, five. I express the following as prime factors in intent form.

26:29 144, express it as the prime factors and 198 and 300. Thank you very much for watching.

26:39 My name is Ayase Sondi. Till next time.