Representing a number as a decimal, percent, and fraction

U05_L1_T1_we3 Representing a number as a decimal, percent, and fraction

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.