Ordering numeric expressions

Ordering numbers expressed as decimals, fractions, and percentages

Welcome to the presentation
on ordering numbers.

Let's get started with some
problems that I think, as you

go through the examples
hopefully, you'll understand

how to do these problems.

So let's see.

The first set of numbers that
we have to order is 35.7%,

108.1% 0.5, 13/93,
and 1 and 7/68.

So let's do this problem.

The important thing to remember
whenever you're doing this type

of ordering of numbers is to
realize that these are all just

different ways to represent--
these are all a percent or a

decimal or a fraction or a
mixed-- are all just different

ways of representing numbers.

It's very hard to compare when
you just look at it like this,

so what I like to do is I
like to convert them

all to decimals.

But there could be someone who
likes to convert them all to

percentages or convert them all
to fractions and then compare.

But I always find decimals to
be the easiest way to compare.

So let's start with this 35.7%.

Let's turn this into a decimal.

Well, the easiest thing to
remember is if you have a

percent you just get rid of
the percent sign and

put it over 100.

So 35.7% is the same
thing as 35.7/100.

Like 5%, that's the same thing
as 5/100 or 50% is just

the same thing as 50/100.

So 35.7/100, well, that
just equals 0.357.

If this got you a little
confused another way to think

about percentage points is if I
write 35.7%, all you have to do

is get rid of the percent sign
and move the decimal to the

left two spaces and
it becomes 0.357.

Let me give you a couple of
more examples down here.

Let's say I had 5%.

That is the same
thing as 5/100.

Or if you do the decimal
technique, 5%, you could just

move the decimal and you
get rid of the percent.

And you move the decimal over 1
and 2, and you put a 0 here.

It's 0.05.

And that's the same
thing as 0.05.

You also know that 0.05 and
5/100 are the same thing.

So let's get back
to the problem.

I hope that distraction didn't
distract you too much.

Let me scratch out all this.

So 35.7% is equal to 0.357.

Similarly, 108.1%.

Let's to the technique where we
just get rid of the percent and

move the decimal space over
1, 2 spaces to the left.

So then that equals 1.081.

See we already know that
this is smaller than this.

Well the next one is easy,
it's already in decimal form.

0.5 is just going to
be equal to 0.5.

Now 13/93.

To convert a fraction into
a decimal we just take the

denominator and divide
it into the numerator.

So let's do that.

93 goes into 13?

Well, we know it goes
into 13 zero times.

So let's add a
decimal point here.

So how many times
does 93 go into 130?

Well, it goes into it one time.

1 times 93 is 93.

Becomes a 10.

That becomes a 2.

Then we're going to
borrow, so get 37.

Bring down a 0.

So 93 goes into 370?

Let's see.

4 times 93 would be 372,
so it actually goes into

it only three times.

3 times 3 is 9.

3 times 9 is 27.

So this equals?

Let's see, this equals-- if we
say that this 0 becomes a 10.

This become a 16.

This becomes a 2.

81.

And then we say, how many
times does 93 go into 810?

It goes roughly 8 times.

And we could actually keep
going, but for the sake of

comparing these numbers, we've
already gotten to a pretty

good level of accuracy.

So let's just stop this problem
here because the decimal

numbers could keep going on,
but for the sake of comparison

I think we've already got a
good sense of what this

decimal looks like.

It's 0.138 and then
it'll just keep going.

So let's write that down.

And then finally, we have
this mixed number here.

And let me erase some of
my work because I don't

want to confuse you.

Actually, let me keep it
the way it is right now.

The easiest way to convert a
mixed number into a decimal is

to just say, OK, this is 1
and then some fraction

that's less than 1.

Or we could convert it to a
fraction, an improper fraction

like-- oh, actually there are
no improper fractions here.

Actually, let's do it that way.

Let's convert to an improper
fraction and then convert

that into a decimal.

Actually, I think I'm going to
need more space, so let me

clean up this a little bit.

There.

We have a little more
space to work with now.

So 1 and 7/68.

So to go from a mixed number to
an improper fraction, what you

do is you take the 68 times 1
and add it to the

numerator here.

And why does this make sense?

Because this is the same
thing as 1 plus 7/68.

1 and 7/68 is the same
thing as 1 plus 7/68.

And that's the same thing as
you know from the fractions

module, as 68/68 plus 7/68.

And that's the same thing
as 68 plus 7-- 75/68.

So 1 and 7/68 is
equal to 75/68.

And now we convert this to a
decimal using the technique

we did for 13/93.

So we say-- let me
get some space.

We say 68 goes into 75--
suspicion I'm going

to run out of space.

68 goes into 75 one time.

1 times 68 is 68.

75 minus 68 is 7.

Bring down the 0.

Actually, you don't have to
write the decimal there.

Ignore that decimal.

68 goes into 70 one time.

1 times 68 is 68.

70 minus 68 is 2,
bring down another 0.

68 goes into 20 zero times.

And the problem's going to keep
going on, but I think we've

already once again, gotten to
enough accuracy that

we can compare.

So 1 and 7/68 we've now figured
out is equal to 1.10-- and if

we kept dividing we'll keep
getting more decimals of

accuracy, but I think we're
now ready to compare.

So all of these numbers I just
rewrote them as decimals.

So 35.7% is 0.357.

108.1%-- ignore this for
now because we just used

that to do the work.

It's 108.1% is equal to 1.081.

0.5 is 0.5.

13/93 is 0.138.

And 1 and 7/68 is 1.10
and it'll keep going on.

So what's the smallest?

So the smallest is
0.-- actually, no.

The smallest is right here.

So I'm going to rank them
from smallest to largest.

So the smallest is 0.138.

Then the next largest
is going to be 0.357.

Then the next largest
is going to be 0.5.

Then you're going to have 1.08.

And then you're going
to have 1 and 7/68.

Well, actually, I'm going to do
more examples of this, but for

this video I think this is the
only one I have time for.

But hopefully this gives you a
sense of doing these problems.

I always find it easier
to go into the decimal

mode to compare.

And actually, the hints
on the module will

be the same for you.

But I think you're ready at
least now to try the problems.

If you're not, if you want to
see other examples, you might

just want to either re-watch
this video and/or I might

record some more videos with
more examples right now.

Anyway, have fun.