-
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.