Ordering numeric expressions

Ordering numbers expressed as decimals, fractions, and percentages

Welcome to the presentation on ordering numbers.

Lets 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 precent or a decimal or a fraction or

a mixed number--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, you know,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 precent 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.

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 samller 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. Right?

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, we 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.

So these two ways

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. Right?

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 samllest?

So the samllest is 0.

Actually, the smallest is right here.

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

So the samllest is 0.138.

Then the next largest is going to be 0.357. Right?

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.

So hopefully, 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.