00:10 Hello, I'm Oyase Sunday, and I'm taking Matamatics JSS 3 class.

00:18 We're treating an interesting topic for today.

00:22 And the topic is rational and non-rational numbers.

00:26 We're taking it from the numbers and numerations.

00:29 Now what I'm looking at, the number of numerations is a broader cycle of numbers.

00:34 So we have rational, irrational numbers, we have percentage, we have number base.

00:40 Everything could go up together on the numbers and numerations.

00:44 Now, we're moving in.

00:46 What's the objective of this class?

00:50 The objective of this class is to identify what are rational numbers and what are those irrational numbers.

00:56 And to determine particle appropriate values for the PI, the PI.

01:02 Now, the PI is usually used doing what?

01:07 A cycle, that's the cycle phase of the cycle, to bring in your PI.

01:11 How do we determine that?

01:12 Now, move on straight up to number set.

01:16 Number set is a group of numbers that have similar properties.

01:21 A group of numbers that have similar properties are called a number set.

01:24 So the fed of a set is a group of things that have similar properties.

01:28 So a group of numbers that have similar properties are called set of numbers.

01:33 Now, what are the types of numbers?

01:35 We have the natural numbers.

01:36 The natural numbers are the numbers that include a positive counting numbers.

01:42 They're natural numbers.

01:43 They include the positive counting numbers.

01:44 So you talk about your 1, your 2, your 3, your 4, your 5.

01:48 As far as this is positive and this is counting number, it is called a natural number.

01:54 Take note of that, because we're still going to come back to it.

01:57 Now, we have the O number.

01:58 The O number is a set of numbers that include all positive counting numbers and the zero.

02:03 For natural numbers, the zero is not part of it.

02:06 For the O numbers, we have from zero, 1, 2, 3.

02:12 The difference between the O numbers and natural numbers is the zero.

02:16 That's included.

02:17 Take a look.

02:17 The zero included mixed the numbers to become what O.

02:22 Then we have what we call the integers.

02:24 Now, what are they?

02:25 They are the set of numbers that include the negative counting numbers

02:29 and the zero, negative counting numbers and the zero plus positive numbers.

02:33 So let me take an instance into it.

02:36 So you could have a clearer example.

02:37 Let me have an insight into the numbers.

02:42 So because all we'll be discussing in this topic will be numbers, numbers, and numbers.

02:48 Let me have minus three, minus two, minus one, zero, one, two, and three.

02:57 Now, take note.

02:59 One, two, three, these are called natural numbers because they are counting numbers

03:05 and they are positive in value.

03:08 Adept is zero to the collection. It becomes an O number.

03:13 When you now add that your negativity numbers to eat, it becomes an integers.

03:18 So what does that mean?

03:19 From the negative to the whole and to the natural.

03:23 A collection of them gives you what integers.

03:26 Don't forget, very important.

03:28 Now, what are two set of numbers that we can have?

03:31 We can have the set of rational numbers and the set of non-rational numbers,

03:36 that are non-rational.

03:38 Now, what are the rational numbers?

03:39 The rational numbers are the set of numbers.

03:42 All numbers that are written in the form of A over B,

03:47 such that A and B are both integer and B is not equal to zero.

03:52 That means B is not equal to zero.

03:56 When B is equal to zero, it's no longer a rational number.

03:59 So a rational number is expected to have in the form of a fraction,

04:03 but the B is not expected to be equal to what?

04:08 Zero.

04:08 We have a lot of numbers.

04:10 So we have fractions in rational number.

04:12 We have percentage.

04:13 We have the likes of orders.

04:15 They fall under rational numbers.

04:17 Why the irrational numbers, irrational numbers are all the numbers

04:21 that are not parts of the set of rational numbers.

04:24 They are the numbers that are not part of the set of rational numbers.

04:28 They are separated.

04:29 They are the numbers that are not included into the set of rational numbers.

04:34 So the question is, what are the examples of rational numbers?

04:37 Like I said, the integers, I've introduced that before,

04:40 that all the values are what rational numbers.

04:44 Remember, rational number has to have an A and a B,

04:47 and the B is not equal to zero.

04:49 So if I'm to have a number where I have A over B,

04:54 B is not equal to zero.

04:57 No matter what this number is and this is,

05:00 they fall into the category of rational numbers.

05:03 So what does that mean?

05:05 So we have integers.

05:06 They are all rational numbers.

05:07 Integers are all rational numbers.

05:09 This is because any integer within in a fraction form with one

05:12 I did not know therefore it becomes what irrational numbers.

05:16 So you have A to 1, 125 to 1, 125 to 1, 125 to 1, 6,

05:21 125, 129, 129, 129, if I'm dividing to you.

05:24 Remember, the B must not be equal to zero.

05:26 So once the B is not equal to zero,

05:28 whatsoever you have at the top,

05:30 it goes to be what?

05:32 A word, an integer, and which is example of rational number.

05:36 Now, we have the common fractions.

05:38 All fractions, all common fractions are rational numbers.

05:41 All common fractions, whether it's an improper fraction,

05:44 whether it's a proper fraction,

05:45 whether it's a mixed fraction,

05:47 they all fall on that the categories

05:50 of what rational numbers.

05:52 Like I said, the proper fraction,

05:53 they do not need all, is smaller compared to the numerator.

05:59 Remember, as a fraction,

06:01 like we know that the fraction

06:03 has must have a numerator and a denominator.

06:06 So the A here represents what?

06:09 The numerator and the B here represent a denominator.

06:13 So what makes it a proper fraction?

06:15 This is when the numerator is smaller compared to the denominator.

06:21 That means the denominator is bigger than the numerator.

06:24 So the numerator is expected to be smaller.

06:25 So I have 3 over 8.

06:28 I have 11 over 20.

06:30 You could see that 11 smaller compared to 20.

06:32 I have 17 over 18 at the rest of the others.

06:35 Now, that is the proper fraction.

06:37 Now, an improper fraction is the opposite direction,

06:41 opposite direction in the sense that

06:43 the numerator here is what is larger than the denominator.

06:48 Now, remember that the numerator there was smaller,

06:51 but the A is now larger.

06:53 So I can have here now over 7.

06:56 I can have 11 over 10.

06:58 You see the up one becomes bigger than the smaller one.

07:01 It becomes improper.

07:03 Then the misfraction is a combination of what?

07:06 O number, that's O number and a proper fraction.

07:09 And a combination of O number and a proper fraction.

07:13 That gives us the misfraction.

07:14 So if I have an example, I have 1,

07:18 O number, 3 over 2.

07:20 This is a misfraction.

07:23 I call this a misfraction.

07:24 In the sense that you can see that it's a combination

07:27 of both O numbers and what?

07:31 And the what?

07:32 The proper fraction.

07:35 One O number, two over 3.

07:38 Now, this is a what?

07:40 Missed what?

07:41 Missed numbers.

07:42 Now, remove.

07:44 Hopefully, first say, that's the percentage.

07:47 Our percentage are rational numbers.

07:50 Like I said, from the beginning, I said,

07:51 rational number has a larger volume of the numbers.

07:56 A larger volume of O numbers are inside the rational numbers,

08:00 the larger volume.

08:00 So we have percentage.

08:02 We have fractions.

08:03 Fractions.

08:04 Percentage are inside the rational numbers.

08:08 Take it off.

08:09 So we have percentage.

08:11 I said, all percentage are rational numbers.

08:13 A percentage is a fraction of which denominator is 100.

08:18 And where only the numerator is written down,

08:21 followed by a percentage symbol.

08:24 A percentage.

08:25 A percentage is written in a percentage form.

08:28 That means an on-dread form.

08:29 So if I have an example, let's give an example

08:33 where I have from I have 3%, 3%.

08:39 Look at the percentage sign.

08:41 The categories of rational numbers, the percentage sign.

08:43 Because of this percentage,

08:44 these three will be expressed in what?

08:46 In on-dread.

08:47 So I will just simply have it as 3 over 100.

08:53 Like this.

08:54 So I have 72%, that's 72 by 100, 120%.

08:59 And what are the percentage?

09:00 So in all categories, they all fall on that award.

09:04 The rational numbers.

09:05 Now, moving ahead to the rational numbers.

09:09 The rational numbers are numbers that cannot be written

09:12 in the form of A, B. That means such A and B

09:16 are both integers and B is not equal to zero.

09:19 That means the rational number

09:21 cannot be written in the form of A, B.

09:22 So rational numbers do not have exact values.

09:26 They don't have an exact value.

09:28 The rational numbers are not that I express

09:30 mostly especially in decimal places.

09:32 They don't have two points.

09:34 You have examples of rational numbers, number one, decimals.

09:37 Decimals, they have indefinite numbers

09:40 of decimal digits, of which none are we occurring.

09:44 So for example, you have 2.5566 and just what that.

09:47 Those have a continuous way of representation.

09:51 And each does not have a real correct nature.

09:55 They all have a different nature.

09:56 If you look to 2.56879, you observe

10:00 that it's not a real correct digit.

10:03 They are what?

10:04 Different.

10:05 We have the good square root.

10:06 Square root does not have all numbers.

10:08 And so terminate decimals or common fractions as what?

10:11 As answers.

10:12 So square root also too.

10:14 As such, this falls under the categories of the award.

10:18 In rational numbers.

10:19 But now we're moving to the pie.

10:22 This is the delicate aspect of the pie.

10:24 The pie has to do with the cycle.

10:26 The cycle falls.

10:27 Now moving up to the cycle form.

10:30 A pie.

10:30 A pie is an example of an irrational numbers.

10:34 Remember, we're starting from rational numbers.

10:36 Where we consider the fractions, the types of fractions.

10:39 Remember.

10:40 Now, we are under the cycle of the irrational numbers.

10:44 Now, the irrational numbers we move to with the pie.

10:46 And the pie is an example of a new rational number.

10:48 It is represented by the simple pie.

10:51 We have this simple pie.

10:54 This simple represents what?

10:56 Pie.

10:57 Now, it's a category of rational numbers.

11:01 And it represents different ratios in a cycle.

11:05 In a cycle form, I have a cycle form.

11:09 I have the middle of the cycle to any part

11:12 that I wish in between the cycle.

11:15 Now, when I have it in this form,

11:18 the pie, the middle of the cycle to any part

11:22 of the cycle that I have.

11:23 Yeah, it's usually called the radios.

11:26 Now, I have for any cycle, pie represents the following.

11:30 Pie represents the cycle phrase of the cycle.

11:33 Pie represents the pie represent various forms in the cycle.

11:37 So we have second phrase divided by diameter.

11:40 What diameter?

11:41 From here to this point, from the middle

11:44 to any point of the cycle is reduced.

11:46 From any point of the cycle to here,

11:49 so we have radios and I have radios.

11:51 Two radios makes one diameter.

11:53 So I have diameter is two radios.

11:58 Two radios makes one diameter.

12:00 So if I'm calculating for my pie, for example,

12:04 my pie will give me second phrase of the cycle,

12:08 that the second phrase of the cycle

12:10 all divided by the diameter.

12:14 That means I'm dividing the second phrase by the diameter.

12:18 Remember, the diameter is two radios.

12:19 So I could also say what?

12:21 But the second phrase divided by two radios.

12:25 That's a pie.

12:25 So I have my pie.

12:27 The pie do not have a fixed value.

12:29 I've said, does not have a fixed value.

12:31 They can be used in a calculator.

12:32 You can have your calculator.

12:33 You can point it to a calculator to give you

12:35 3.142 or 22 of a seven.

12:38 That's commonly used.

12:40 That O to have, but it's not that it has a specific value.

12:44 But for the purpose of computation,

12:47 for the purpose of computation,

12:48 we'll decide to represent pie to be 22 over seven.

12:52 Because when you die your calculator and have 22 divided by seven,

12:55 it will give you a 3.4, 222 and there's the products.

13:00 It does not have an exact value.

13:01 Well, we could wrap it up and just make it 22 over seven.

13:05 So for easy introduction into the cycle

13:08 and the order trigonometric form.

13:11 Now, now we are confirming the value of pie.

13:16 We said the cycle below as a circumference of six,

13:19 circumference is given to be 62.83832 centimeter.

13:27 62.832 centimeter.

13:30 The circumference, the circumference of this cycle

13:34 is given to be what?

13:36 62.832 centimeter.

13:40 And an area is given to be 314.16 centimeter squared.

13:48 The radios is given to be 10 centimeters.

13:52 So the question is calculate the radios of the circumference

13:56 to the world, to the diameter, calculate the radios

14:00 of the circumference to the world, to the diameter.

14:02 The first question is, look at this question, category, calculate.

14:06 What do I need?

14:07 The question is, what do I need?

14:10 Remember, we said that when calculating, we have what?

14:14 When calculating?

14:16 We have our circumference of the cycle.

14:19 Our circumference of the cycle is given to be what is given to be C.

14:25 We are looking for the pie of any given, express cycle question

14:33 is circumference over diameter.

14:35 And I also say that which could also be circumference over 2R.

14:44 2R means 2 radios makes 1 diameter.

14:49 So if I'm given the radios here to be 10 centimeter,

14:53 and I am given my circumference to be 62.8.62.832 centimeter.

15:03 So I put it.

15:04 So simply, move it.

15:06 I have my pie is what my circumference is given.

15:13 The circumference is given in 62.832 over what's my radios?

15:22 My radios is 10.

15:23 That is 10.

15:25 Now, I have 2 radios makes 1 diameter.

15:28 That's times 2.

15:30 I multiply by 2.

15:33 Now, I am looking for the pie.

15:35 So, category, category, move it upward a bit.

15:39 So I could have this multiply, go to your calculator, that's 62.832 over 20.

15:51 When you divide it by 20, when you bring out your calculator and you divide this by 20,

15:56 you are expected to have your pie to be 1.

16:03 3.1416, 3.1416, 3.1416.

16:18 Now, that becomes my value when you divide it on your calculator.

16:25 Just pick up your calculator and say, okay, up to 2.832 divided by 20.

16:31 You have 3.1416.

16:34 Now, you could calculate the radios of 3.1416.

16:41 Now, look at that question number 2.

16:45 We have question number 2.

16:47 Question number 2 says, calculate the ratio of the area to the square of the radios.

16:56 Calculate the ratio of the area to the square of the radios.

17:03 Now, how do you do that?

17:04 Remember that our area has been given to be 3.14.6.

17:14 That's the area.

17:15 And we have our radios has been given to be 10 centimeter.

17:22 Now, we are asked to calculate what are they expecting to do.

17:27 Now, when you are calculating the ratio of the area to the square of the radios,

17:34 this is what you do.

17:36 The ratio of the area to the square of the radios, so now let's go.

17:39 When you are doing that, what you are simply going to be doing here is

17:43 the ratio of the area to give us area over the radios square.

17:49 Area over the radios square.

17:52 And what's our area?

17:54 Our area is already given to be 3.14.4.314.4.1.6.

18:08 And our radios is given to be 10 square.

18:13 That's 10 times 10.

18:14 10 in two forms.

18:16 That's 10 times 10.

18:18 10 in two form. 10 times 10.

18:20 10 times 10.

18:22 Now, going forward, we have that gives

18:28 categorically equal to 3.14.1.6 divided by 10 times 10 is 100.

18:40 100.

18:41 So, we have 3.14.1.6 divided by 100 would give 3.14.1.6.

18:55 3.14.1.6 when you do your mathematical calculation.

19:01 Now, with these two examples, we will give you an idea

19:05 to what pi equation or pi really means.

19:10 Now, you have some questions, which I expect you to do.

19:14 You have said calculate 16 divided by 9 in 3 decimal places.

19:21 16 divided by 9 in 3 decimal places.

19:26 And write 0.3 as a rational number.

19:31 That's transformed the form it is into a rational form.

19:35 So, transform, write 0.3 as a rational number.

19:43 That's true, what you expected to do.

19:46 Thank you very much, we've come to the end of this class.

19:49 I remain Oyase Ose Sunday.

19:52 See you in the next class.