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We're asked to write 7/8 as a decimal and as a percent.

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We'll start off with a decimal, and we'll see it's

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pretty easy to go from a decimal to a percent.

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Now, whenever you see a problem like this, it's

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sometimes confusing.

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It's like, how do I even get it into a decimal, or as a

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fraction over 100, or as a percentage?

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And you always have to remember 7 over 8, or 7/8, is

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the exact same thing.

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This means literally 7 divided by 8.

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Not 8 divided by 7.

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7 divided by 8.

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The numerator divided by the denominator.

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And you say, well, how do I turn that into a decimal?

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Well, we just literally do a long division problem, but we

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keep going behind the decimal point, so that we don't end up

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with a remainder, or until we end up with things repeating.

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You'll see what we mean.

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In this case, we won't end up with anything repeating.

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So let's try this out.

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So it's 7 divided by 8.

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So how many times does 8 go into 7?

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Well, 8 does not go into 7.

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It goes zero times.

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And actually, just so that we make sure that everything's

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clean, let's put our decimal.

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You can view this as 8 going into 7.000.

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You can keep adding as many zeroes as you need until

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you're done dividing.

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So we have our decimal point right here, right behind the 7

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where it was up here.

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So we say 8 goes into 7 zero times.

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0 times 8 is 0.

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You subtract.

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7 minus 0 is 7.

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Now we can bring down a 0.

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We bring down a 0.

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It becomes 70.

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And then you say 8 goes into 70 how many times?

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Well, 8 times 8 is 64, so that works.

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8 times 9 is 72.

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That's too big.

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So it goes into it eight times.

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8 times 8 is 64.

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When you subtract, 70 minus 64 is 6.

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You still have a remainder, so let's keep going.

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Let's bring down another 0.

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So you bring down another 0 right over there, and so you

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say, how many times does 8 go into 60?

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8 times 8 is 64, so that's too big.

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8 times 7 is 56, so that'll work.

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So it goes into 60 seven times.

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7 times 8 is 56.

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You subtract.

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60 minus 56 is 4.

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So we still have a remainder, so let's keep bringing down

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some zeroes.

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So let's bring this 0 down here.

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And 8 goes into 40 how many times?

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Well, 8 times 5 is 40, so it goes in nice and evenly.

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So it goes into it five times.

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5 times 8 is 40.

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Subtract.

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No remainder.

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So as a decimal, we just figured out that 7/8, which is

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equal to 7 divided by 8, is exactly 0.875.

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So 7/8 as a decimal is equal to 0.875.

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Now we've done the decimal part.

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Now the next thing is to do a percent.

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And if you have it as a decimal, doing it as a percent

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is very easy.

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You literally shift the decimal place two to the

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right, and you put a percent sign there.

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And I think it makes sense why it works.

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Now you're going to say, how many per hundred?

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You can view this as 875 thousandths.

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Let me write this down.

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You can view this as a fraction.

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You could say, well, this is the same thing as 875/1,000.

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That's how we've read it in the past. This is the

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thousandths spot right here.

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Or you could read this as 87.5/100.

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If you just go two decimal places, it's 87.5/100.

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Or if you just took this, and you divide the numerator and

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the denominator by 10, you would get this.

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And this is literally saying 87.5 per 100, So this second

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statement right here, this is literally saying 87.5 per

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hundred, or per cent.

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So this is equal to 87.5%.

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So that gives you the reasoning for why it works,

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but the really easy way, if you have a decimal, to make it

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into a percent, you literally multiply the number by 100 and

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put the percent there, which is essentially telling you

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that you're going to divide by 100, so you're multiplying and

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dividing by 100.

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So if you multiply this by 100, which is equivalent to

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shifting the decimal place two places to the right, that

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literally would become 87.5, then you

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want to put the percent.

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This says this is going to be over 100.

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So you multiply by 100, and then divide by 100.

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You're not really changing the number.

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Hopefully, that makes sense.

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Another way to remember, because sometimes you might

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get confused-- Do I put the decimal to the right?

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Do I take it to the left-- is that the decimal

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representation will always be smaller than the percent

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representation.

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And not only will it be smaller, but it will be

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smaller by exactly a factor of 100.

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This is 100 times smaller of a number right here

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than just the 87.5.

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Obviously, when you put this percent here, these become the

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exact same number.

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