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 thirty-five point seven percent,
one hundred eight point one percent, zero point five, thirteen over ninety-three, one, and seven over sixty-eight.
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 thirty-five 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 thirty-five point seven percent is the same thing as thirty-five 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 thirty-five point seven over one hundred, well, that
just equals zero point three five seven.
If this got you a little confused,
another way to think about percentage points is if I write thirty-five 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 zero point three five seven.
Let me give you a couple of 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 zero point zero five.
And that's the same thing as zero point zero five.
You also know that zero 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 thirty-five point seven percent is equal to zero point three five seven.
Similarly, one hundred eight point one percent--
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.
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.
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'd get more decimals of accuracy. So we're ready to compare.
So all of these numbers I just
rewrote them as decimals.
So 35.7% is 0.357.
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 . -- 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. 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.
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.