Video 2: Real Number System

So if you take your calculator and you put in one divided by 8, enter or equal, you'll see a 0.125. That is a decimal. So that means that it's not natural, not whole, not an integer, but yes, it is real. All right, what about 8 over one? This means 8 on top, divided by one on the bottom. So let's do that. So I'm going to hit clear. I'm going to do 8 on top. Divided by one on the bottom. And it equals 8. So is 8 a natural number that a child to four years old would naturally count? And the answer is yes. Yes, it's natural. 8 a whole number is a positive number. Yes. It is a whole number. Is 8 an integer that you would find on the number line? Yes. It is an integer. And is 8 a real number? The answer is yes. It is a real number.

Now we have 0.8. Is 0.8 a natural number? No. It is not natural. Is 0.88 whole number. It is not a whole number. Is a 0.8 integer. It is not an integer. And a 0.8, a real number. Yes. It is a real number. All right, square root 8. If you take your calculator, we're looking for the square root button. This little purple button that has the little line that goes down up, it almost looks like a division, long division symbol, has a little X here. This is not the correct square root button. This button that has the line looks like a long division with no number or sometimes it has a number two. This is your square root button. This is your squared button. Square root and squared. Squared is the opposite of square root, square root is the opposite of squared, just like addition is the opposite of subtraction, division is the opposite of multiplication. Squared is a square root or opposites. In order to get to this button, you have to press the purple button to get to the purple buttons.

So I'm going to press this blue or purple button first, and then I'm going to press this button. And as you can see, you have your square root sign. Press the number 8. You can close the parentheses. If you want, it's a good habit to get into and then hit equals. So the square root of 8 is 2.8. Two 8 four two 7 one two 5. So let's ask ourselves is this number is a natural number and the answer is no. So square root 8 is not natural. Is square root 8 2.82 8 is that number a whole number? No. It is not a whole number. Is that number an integer? It's not an integer. It's not something that we'd see on the number line. And it's a real number. Yes. It is. Real. Number. Okay? Two 25 square roots of two 25.

I will hit clear, and I will hit my second button again. Activate that little purple or blue square root. I will hit two 25, I'll close my parentheses. And hit enter. Not all calculus have the parentheses, so don't worry about that. And the answer is 15. Now we're going to ask is 15. A natural number. Is 15 a natural number? Yes, it is. So yes, natural. Is 15 a whole number? Yes. That's a whole number. Is 15 an integer, yes. It's an integer. And it's 15 real numbers. Yes. All numbers that we learn about right now are real numbers.

Now, here we had square root 8. Now we have 8 squares. Remember 8 squared looks like this with a little two in the air. So this little two in the air, that's called squared. If you had 8, with the three in the air, that little three is called Q. 8 squared, 8 cubed. So 8 squared just means 8. Times 8, just 8 two times. So we look at our calculators, by 8 squared, we just do, it really means 8 times 8. Which is 64. So now we're going to ask ourselves is 64? Excuse me, a natural number. The answer is yes. It's natural. In 64, a whole number. Yes. It's a whole number. It's 64 an integer. Yes, it's an integer. And a 64 is a real number. Yes. It is a real number. Excuse me. 21 over 19. So we have 21 on top. We have our division or our fraction line, and then we have 19 at the bottom. Let's see what that does. So we have 21 divided by 19. Equals 1.105263 one