 Okay, in this video, we're going to talk about classifying real numbers. If I can spell real correctly, there we go. Classifying real numbers, I'm just going to do examples because, again, going over a video of just the meaning of the words doesn't make a whole lot of sense unless you actually apply it to a few numbers. So I have the five classifications here. Natural numbers, whole numbers, integers, rational and irrational numbers. Okay, so what I'm going to do is just write a couple of examples here up on the board and we're going to classify them. So we'll start with something simple. We'll start with the number three. Okay, again, a very basic example. But now what we're going to do is we're going to figure out which category this belongs to, which classification does this number belong to. Okay, so remember our natural numbers. Those are also known as the counting numbers. So the numbers you use to count with your ones and twos and threes and fours and fives. So as we can assume, this would be a natural number. Okay, now let's just keep going down the list. A whole number. Now the only difference between natural and whole numbers is you add the number zero in with the whole numbers. So zero, one, two, three, four, five are all the whole numbers. So three is included in that. So this is also a whole number. Okay, going down the list, integer. Integers include the whole numbers and the negative whole numbers. So negative one, negative two, negative three. Okay, three is included in that. So it's also an integer. A rational number. Okay, now this one's a little tough. Rational numbers are the fractions. Any number that you can make into a fraction. So for example three, I can also write three as nine over three. I can write it as 12 over four. I can write it as negative 27 over negative nine. So lots of, all these fractions, they reduce to three. So there's lots of different ways to write three as a fraction. Okay, but just with the knowledge that I can write it as a fraction, that also makes this a rational number. Okay, now last but not least, the irrational. Okay, irrational numbers are the numbers that repeat forever and ever and ever and don't have a pattern to them similar to pi. Well three is actually, is a terminating number. It just stops. There's only one number to it. There's no repeating digits, nothing like that. So it is not an irrational number. Okay, so there's one example. Now what's confusing about this with some students is they think, oh there's only one classification for a number. No, there can actually be multiple. Three is natural. It is whole. It is an integer. And it is a rational number. Okay, so lots of different classifications for one number. Okay, so let's do, let's do something else. Let's do for example, I'll think of a good example here. See on my last video I did the example of one-third. Okay, so we use that. One-third is going to go through this again. Now it's one-third a natural number. Now natural numbers are counting numbers. So no, one-third is not a counting number. We don't count by thirds. We count by ones and twos and threes. It's not a natural number. It's a whole number. No, it's not a whole number either. It's an integer. Again, integers are whole numbers and the negatives. So it's not an integer. It's a rational number. Now remember, rationals are fractions. So we have actually found the first one that works for one-third. It is a rational, rational number. Okay, now rational, is it irrational? Well, we got to think, does it, does it terminate? Is there a, is there a lot of repeating digits with this? One-third, we all know that one-third is also equal to 0.333333. Also known as 0.3 repeating. Okay? There is a pattern to one-third. If you take your calculator, take one divided by three. There is a pattern to it. It's just a repeating threes, 33333. It's not much of a pattern, but it is a pattern. Since there is a pattern to this repetition, that means that this is going to be a rational number. It's not going to be an irrational number. If there wasn't any sort of pattern to it. Again, I refer, I like to reflect and look at, look at pi as one of those irrational numbers. Okay? So actually one-third is just a rational number. That's the only classification that we have. So a lot of your fractions that don't reduce are going to be irrational numbers. Okay. Let's think of another one. Okay, so I mentioned a little bit before your negative numbers. This one I'll do very quickly. Negative five, okay? With this number, again we're going to go through our five different classifications. Negative five is a natural. We don't count by negative five. So nope, it's not a natural number. Is it a whole number? Nope, whole number is zero, one, two, three, four, five, so on and so forth. It's not a whole number. Integer, yes. Integers include the negative numbers. So we found our first classification for negative five. Integer, okay? Is it a rational number? Again, rational, can I make it into a fraction? Well, if I take negative 25 divided by five, that will reduce back to negative five. I can make negative five into a fraction. So it also makes it a rational, rational number. Okay, and then irrational, again, is it repeating? Is it non-terminating? Is there a lot of digits afterwards? Is there no pattern to it? I don't see any of that for an irrational number. So negative five is not an irrational number. Let's just do another one. How about negative point zero, one, two, five, seven, eight, three, nine, twelve, dot, dot, dot. This number I put up here, and again, we're going to go through the same process. Is it a natural number? We don't count by this decimal, so that doesn't work. Is it a whole number? No, whole numbers are zero, one, two, three, four, five, so no, it's not a whole number. Is it an integer? Well, you might think, oh, it's a negative number, but nope, that doesn't make it an integer. It's got to be a whole number. Your negative one, negative two is negative three, negative four, negative five, or zero, one, two, three, four, five, one of those. It doesn't work there. Rational, can I make this into a fraction? Well, if I look at this, there's no repeating pattern to it. Zero, one, two, five, seven, it doesn't repeat at all. I see some of the same digits, but it doesn't necessarily repeat. There's no pattern to this. So actually, this would be an example of an irrational number. This is an irrational number. So again, this is very similar to pi, very similar to some other irrational numbers that we have. So this would be an example of an irrational number. I just wanted to throw one of those in there for the end. Again, these are just a couple of examples of how to classify real numbers. Again, our five classifications, natural, whole, integer, rational, and irrational.