Powers of fractions and decimals
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Exponents of decimals
- [Instructor] What we're going to do in this video is get some practice evaluating exponents of decimals. So let's say that I have 0.2 to the third power. Pause this video, see if you can figure out what that is going to be. Well, this would just mean that if I take something to the third power, that means I take three of that number and I multiply them together. So it's 0.2 times 0.2 times 0.2. Well, what is this going to be equal to? Well, if I take 0.2 times 0.2, that is going to be 0.04. One way to think about it, two times two is four and then I have one number behind the decimal to the right of the decimal here. I have another digit to the right of the decimal right over here, so my product is going to have two digits to the right of the decimal, so it'd be 0.04. And then if I were to multiply that times 0.2, so if I were to multiply that together what is that going to be equal to? Well, four times two is equal to eight and now I have one, two, three numbers to the right of the decimal point, so my product is going to have one, two, three numbers to the right of the decimal point. So now that we've had a little bit of practice with that, let's do another example. So let's say that I were to ask you, what is 0.9 squared? Pause this video and see if you can figure that out. All right, well this is just going to be 0.9 times 0.9. And what's that going to be equal to? Well, you could just say nine times nine is going to be equal to 81, and so, let's see, in the two numbers that I'm multiplying I have a total of one, two numbers, or two digits, to the right of the decimal point so my answer's going to have one, two digits to the right of the decimal point. So put the decimal right over there and I'll put the zero, so 0.81. Another way to think about it is nine-tenths of nine-tenths is 81 hundredths, but there you go. Using exponents, or taking exponents of decimals is the same as when we're taking it of integers. It's just in this case you just have to do a little bit of decimal multiplication.