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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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