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## Equivalent representations of percent problems

Current time:0:00Total duration:3:32

## Video transcript

Write 18% as a decimal and as
a fraction in simplest form. So let's do it as a decimal
first. So 18% is the same thing as 18 per 100,
or 18 per cent. I'm actually separating out the
percent, it's only going to be one word, but
I'm writing it as, literally, per cent. Cent means the same
thing as 100. So this literally means
18 per 100. Actually, I said I would do the
decimal first, but we can start putting it into a fraction
first. 18 per 100 as a fraction literally
means 18/100. We're literally doing the
fraction first. This literally means 18 per 100, or
18 hundredths. From here we can go straight
to a decimal or we could do this fraction in
simplest form. Let's do the decimal first, just
because that's actually what I said I would do first.
Let's do that first. This is the same thing as
18 hundredths. And we know how to write
that in decimal form. It's 0.18. You could view this as 1 tenth
and 8 hundredths, which is the same thing, or 10 hundredths and
8 hundredths, which is 18 hundredths. So this is written
in decimal form. And if we write it as a
simplified fraction, we need to see if there is a common
factor for 18 and 100. And they're both even numbers,
so we know they're both divisible by 2, so let's divide
both the numerator and the denominator by 2. So we have 18 divided by 2
over 100 divided by 2. And we're going to get
18 divided by 2 is 9. 100 divided by 2 is 50. And I don't think these guys
share any common factors. 50 is not divisible by 3. 9 is only divisible
by 3 and 1 and 9. So this is the fraction
in simplest form. So we have 18% is the same thing
as 0.18, which is the same thing, in simplest
form, as 9/50. Now, I went through a lot of
pain here to show you that this really just comes
from the word, from percent, from per 100. But if you ever were to see this
in a problem, the fast way to do this is to immediately
say, OK, if I have 18%, you should immediately say,
anything in front of the percent-- that's that anything,
whatever this anything is-- it should be
equal to that anything. In this case it's 18/100. And another way to think
about it, you could view this as 18.0%. I just added a trailing zero
there, just so that you see the decimal, really. But if you want to express this
as a decimal without the percent, you just move
the decimal to the left two spaces. So if we move the decimal to the
left two spaces, one, two, this becomes 0.18. Or you could immediately
say that 18% as a fraction is 18/100. When you put it in simplified
form, it's 9/50. But you should also see that
18/100, and we have seen this, is the exact same thing as
18 hundredths, or 0.18. Hopefully, this made some
connections for you and didn't confuse you.