Representing a number as a decimal, percent, and fraction 2

U05_L1_T1_we4 Representing a number as a decimal, percent, and fraction 2

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

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

pretty easy to go from a
decimal to a percent.

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

sometimes confusing.

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

fraction over 100, or
as a percentage?

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

the exact same thing.

This means literally
7 divided by 8.

Not 8 divided by 7.

7 divided by 8.

The numerator divided
by the denominator.

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

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

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

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

You'll see what we mean.

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

So let's try this out.

So it's 7 divided by 8.

So how many times does
8 go into 7?

Well, 8 does not go into 7.

It goes zero times.

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

clean, let's put our decimal.

You can view this as
8 going into 7.000.

You can keep adding as many
zeroes as you need until

you're done dividing.

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

where it was up here.

So we say 8 goes into
7 zero times.

0 times 8 is 0.

You subtract.

7 minus 0 is 7.

Now we can bring down a 0.

We bring down a 0.

It becomes 70.

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

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

8 times 9 is 72.

That's too big.

So it goes into it
eight times.

8 times 8 is 64.

When you subtract,
70 minus 64 is 6.

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

Let's bring down another 0.

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

say, how many times
does 8 go into 60?

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

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

So it goes into 60
seven times.

7 times 8 is 56.

You subtract.

60 minus 56 is 4.

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

some zeroes.

So let's bring this
0 down here.

And 8 goes into 40
how many times?

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

So it goes into it five times.

5 times 8 is 40.

Subtract.

No remainder.

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

equal to 7 divided by
8, is exactly 0.875.

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

Now we've done the
decimal part.

Now the next thing is
to do a percent.

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

is very easy.

You literally shift the decimal
place two to the

right, and you put a
percent sign there.

And I think it makes
sense why it works.

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

You can view this as
875 thousandths.

Let me write this down.

You can view this
as a fraction.

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

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

thousandths spot right here.

Or you could read this
as 87.5/100.

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

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

the denominator by 10,
you would get this.

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

statement right here, this is
literally saying 87.5 per

hundred, or per cent.

So this is equal to 87.5%.

So that gives you the reasoning
for why it works,

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

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

put the percent there, which
is essentially telling you

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

dividing by 100.

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

shifting the decimal place two
places to the right, that

literally would become
87.5, then you

want to put the percent.

This says this is going
to be over 100.

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

You're not really changing
the number.

Hopefully, that makes sense.

Another way to remember, because
sometimes you might

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

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

representation will always be
smaller than the percent

representation.

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

smaller by exactly
a factor of 100.

This is 100 times smaller
of a number right here

than just the 87.5.

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

exact same number.