![]() Square root of nine over seven is the same thing as three-sevenths. This is the same thing as, square root of nine is three, it's the principal root of Well, what's the principal root of nine? This thing is gonna be the same thing, this thing is the same. ![]() See, you have the square root of nine over. These two things areĪctually the same number, just different ways of representing them. It's not a whole numberīecause it's negative, but it's an integer. So, this is just another representation of this, right over here. So, this thing is going to be, this thing is going to beĮquivalent to negative five. Square root of that's just gonna be five. I've been consistent, relatively consistent, with the colors. If you looked at itsĭecimal representation, it will never repeat. So if we just take a multiple of pi, if we just take a integer multiple of pi, like that, this is also going The same thing as two, that is a whole number. ![]() You could have represent this as just two. Integers, it doesn't need to be represented as the It doesn't look like a whole number, but, remember, a whole number is a non-negative number that doesn't need to be represented as the But if you think about it, 14 over seven, that's another way of saying, 14 over seven is the same thing as two. It'll just keep being new and new digits. This will be, if you were to represent it as a decimal, it will not repeat. I'm not proving it to you here, but you cannot represent this as the ratio of two integers, or aįraction with two integers, with an integer in the numerator and an integer in the denominator. So, any square root ofĪ non-perfect square is going to be irrational. It could have been an integer, but we'll throw it up It either as a decimal or a fraction of integers. But, for our sake, we just know that this can be representedĪs a fraction of two integers just the way that 0.3, repeating, can be. And later on, we're gonna see techniques of how do you convert this toĪ fraction of two integers. Not going to do it here, just for the sake of time, but, for example, 0.3, repeating, that's the same thing as one-third. 1313, or you have the 0.27131313, any number like this can be Now, you might not realize it yet, but any number that repeats eventually, this one does repeat eventually, you have the. This is the same thing as 0.27131313, that's what line up there represents. So, this, right over here, this would also be a rational number, but it's not an integer, Or some type of decimal that might repeat. I can't somehow make this without using a fraction Represent this any other, except as a fraction of two integers. Represented, already, as a fraction of two integers, but I don't think I can So, 0.25 is a rational number, but it's not an integerĪnd not a whole number. But there's no way to represent this except using a fraction of two integers. So, we can represent that as a fraction of two integers, I should say. To be a rational number, but it's not a whole numberīecause it is negative. It's an integer, and if you're an integer, you're definitely going Now, negative five, onceĪgain, it can be represented as a fraction, but it doesn't have to be, but it is negative. Number, it's an integer, and it's a rational number. You're also an integer, and you're also a rational number. It, literally, could be justĪ three, right over there, but it's also non-negative. Where would you put them on this diagram? So, let's start off with three. See if you can figure out what category these numbers fall into. These categories in place, let's categorize them. The rational numbers." All right, now that we have Just think about the rational." I'd say, "Let's think about "Let's think about the integers." But I wouldn't say, "Let's So, these are going toīe the whole numbers. So let me do that subset, right over here. The non-negative integers, you're then talking about whole numbers. So, integers are numbers that don't have to be represented as aįraction or a decimal. So, I'll do that in, let meĭo that in this blue color. And then, within rational numbers, you have integers themselves. Represented as a fraction of two integers. Infinite number of rational and an infinite number And the size of these circles don't show how large these sets are. Represented as a fraction of two integers, weĬall irrational numbers. Represented as a fraction of two integers, we call So, let's call these, or the standard way of calling these things. So this circle, over here, this represents all of the numbers that can be represented as the fraction of two integers, and, ofĬourse, the denominator can't be equal to zero,īecause we don't know what it means to put a Of number categories, and let me draw the categories. Is to see if we can classify them into different types Bunch of numbers listed up here, and my goal, in this video,
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