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Representing a number as a decimal, percent, and fraction 2

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We're asked to write 7/8 as a decimal and as a percent. We'll start off with a decimal, and we'll see it's pretty easy to go from a decimal to a percent. Now, whenever you see a problem like this, it's sometimes confusing. It's like, how do I even get it into a decimal, or as a fraction over 100, or as a percentage? And you always have to remember 7 over 8, or 7/8, is the exact same thing. This means literally 7 divided by 8. Not 8 divided by 7. 7 divided by 8. The numerator divided by the denominator. And you say, well, how do I turn that into a decimal? Well, we just literally do a long division problem, but we keep going behind the decimal point, so that we don't end up with a remainder, or until we end up with things repeating. You'll see what we mean. In this case, we won't end up with anything repeating. So let's try this out. So it's 7 divided by 8. So how many times does 8 go into 7? Well, 8 does not go into 7. It goes zero times. And actually, just so that we make sure that everything's clean, let's put our decimal. You can view this as 8 going into 7.000. You can keep adding as many zeroes as you need until you're done dividing. So we have our decimal point right here, right behind the 7 where it was up here. So we say 8 goes into 7 zero times. 0 times 8 is 0. You subtract. 7 minus 0 is 7. Now we can bring down a 0. We bring down a 0. It becomes 70. And then you say 8 goes into 70 how many times? Well, 8 times 8 is 64, so that works. 8 times 9 is 72. That's too big. So it goes into it eight times. 8 times 8 is 64. When you subtract, 70 minus 64 is 6. You still have a remainder, so let's keep going. Let's bring down another 0. So you bring down another 0 right over there, and so you say, how many times does 8 go into 60? 8 times 8 is 64, so that's too big. 8 times 7 is 56, so that'll work. So it goes into 60 seven times. 7 times 8 is 56. You subtract. 60 minus 56 is 4. So we still have a remainder, so let's keep bringing down some zeroes. So let's bring this 0 down here. And 8 goes into 40 how many times? Well, 8 times 5 is 40, so it goes in nice and evenly. So it goes into it five times. 5 times 8 is 40. Subtract. No remainder. So as a decimal, we just figured out that 7/8, which is equal to 7 divided by 8, is exactly 0.875. So 7/8 as a decimal is equal to 0.875. Now we've done the decimal part. Now the next thing is to do a percent. And if you have it as a decimal, doing it as a percent is very easy. You literally shift the decimal place two to the right, and you put a percent sign there. And I think it makes sense why it works. Now you're going to say, how many per hundred? You can view this as 875 thousandths. Let me write this down. You can view this as a fraction. You could say, well, this is the same thing as 875/1,000. That's how we've read it in the past. This is the thousandths spot right here. Or you could read this as 87.5/100. If you just go two decimal places, it's 87.5/100. Or if you just took this, and you divide the numerator and the denominator by 10, you would get this. And this is literally saying 87.5 per 100, So this second statement right here, this is literally saying 87.5 per hundred, or per cent. So this is equal to 87.5%. So that gives you the reasoning for why it works, but the really easy way, if you have a decimal, to make it into a percent, you literally multiply the number by 100 and put the percent there, which is essentially telling you that you're going to divide by 100, so you're multiplying and dividing by 100. So if you multiply this by 100, which is equivalent to shifting the decimal place two places to the right, that literally would become 87.5, then you want to put the percent. This says this is going to be over 100. So you multiply by 100, and then divide by 100. You're not really changing the number. Hopefully, that makes sense. Another way to remember, because sometimes you might get confused-- Do I put the decimal to the right? Do I take it to the left-- is that the decimal representation will always be smaller than the percent representation. And not only will it be smaller, but it will be smaller by exactly a factor of 100. This is 100 times smaller of a number right here than just the 87.5. Obviously, when you put this percent here, these become the exact same number.