
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 thirtyfive point seven percent,

one hundred eight point one percent,

point five,

thirteen over ninetythree,

and one and seven sixtyeighths.

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 mixed numbers

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 thirtyfive point seven percent.

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 one hundred.

So thirtyfive point seven percent is the same thing as thirtyfive point seven over one hundred.

Like five percent, that's the same thing as five over one hundred,

or fifty percent is just the same thing as fifty over one hundred.

So thirtyfive point seven over one hundred, well, that
just equals point three five seven.

If this got you a little confused,

another way to think about percentage points is if I write thirtyfive point seven percent,

all you have to do is get rid of the percent sign and move the decimal to the left two spaces,

and it becomes point three five seven.

Let me give you a couple more examples down here.

Let's say I had five percent.

That is the same thing as five over one hundred.

Or if you do the decimal technique, five percent,

you could just move the decimal and you get rid of the percent.

And you move the decimal over one and two, and you put a zero here.

It's point zero five.

And that's the same thing as point zero five.

You also know that point zero five and five over one hundred 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 thirtyfive point seven percent is equal to point three five seven.

Similarly, one hundred eight point one percent

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

and move the decimal space over one, two spaces to the left.

So then that equals one point zero eight one.

See we already know that this is smaller than this.

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

Point five is just going to be equal to point five.

Now thirteen over ninetythree.

To convert a fraction into a decimal,

we just take the denominator and divide it into the numerator.

So let's do that.

Ninetythree goes into thirteen?

Well, we know it goes into thirteen zero times.

So let's add a decimal point here.

So how many times does ninetythree go into one hundred thirty?

Well, it goes into it one time.

One times ninetythree is ninetythree.

Becomes a ten.

That becomes a two.

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

Bring down a zero.

So ninetythree goes into three hundred seventy?

Let's see.

Four times ninetythree would be three hundred seventytwo,

so it actually goes into it only three times.

Three times three is nine.

Three times nine is twentyseven.

So this equals?

Let's see, this equals if we say that this zero becomes a ten.

This become a sixteen.

This becomes a two.

Eightyone.

And then we say, how many times does ninetythree go into eight hundred ten?

It goes roughly eight 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 point one three eight 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,

okay, this is one and then some fraction that's less than one.

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 one and seven sixtyeighths.

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

what you do is you take the sixtyeight times one

and add it to the numerator here.

Why does this make sense?

Because this is the same thing as one plus seven over sixtyeight.

One and seven sixtyeighths is the same thing as one plus seven over sixtyeight.

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

as sixtyeight over sixtyeight plus seven over sixtyeight.

And that's the same thing as sixtyeight plus seven seventyfive over sixtyeight.

So one and seven sixtyeighths is
equal to seventyfive over sixtyeight.

And now we convert this to a decimal

using the technique we did for thirteen over ninetythree.

So we say let me get some space.

Sixtyeight goes into seventyfive one time.

One times sixtyeight is sixtyeight.

Seventyfive minus sixtyeight is seven.

Bring down the zero.

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

Ignore that decimal.

Sixtyeight goes into seventy one time.

One times sixtyeight is sixtyeight.

Seventy minus sixtyeight is two, bring down another zero.

Sixtyeight goes into twenty 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 one and seven sixtyeighths, we've now figured out, is equal to one point one zero

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 thirtyfive point seven percent is point three five seven.

One hundred eight point one percent is equal to one point zero eight one.

Point five is point five.

Thirteen over ninetythree is point one three eight.

And one and seven sixtyeighths is one point one zero and it'll keep going on.

So what's the smallest?

So the smallest is actually, no

The smallest is right here.

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

So the smallest is point one three eight.

Then the next largest is going to be point three five seven. Right?

Then the next largest is going to be point five.

Then you're going to have one point zero eight.

And then you're going to have one and seven sixtyeighths.

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 do 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 rewatch this video,

and/or I might record some more videos with more examples right now.

Anyway, have fun!