## 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.
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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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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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Title:
Representing a number as a decimal, percent, and fraction 2
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U05_L1_T1_we4 Representing a number as a decimal, percent, and fraction 2

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