WEBVTT

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Welcome to the presentation
on ordering numbers.

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

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go through the examples
hopefully, you'll understand

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how to do these problems.

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So let's see.

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

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

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So let's do this problem.

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

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

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

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

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ways of representing numbers.

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

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

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all to decimals.

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

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percentages or convert them all
to fractions and then compare.

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

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So let's start with this 35.7%.

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Let's turn this into a decimal.

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

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percent you just get rid of
the percent sign and

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put it over 100.

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

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

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the same thing as 50/100.

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

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If this got you a little
confused another way to think

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

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

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left two spaces and
it becomes 0.357.

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

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Let's say I had 5%.

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That is the same
thing as 5/100.

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

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move the decimal and you
get rid of the percent.

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

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It's 0.05.

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And that's the same
thing as 0.05.

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

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So let's get back
to the problem.

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

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Let me scratch out all this.

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So 35.7% is equal to 0.357.

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Similarly, 108.1%.

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

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

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So then that equals 1.081.

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See we already know that
this is smaller than this.

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

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0.5 is just going to
be equal to 0.5.

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Now 13/93.

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To convert a fraction into
a decimal we just take the

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denominator and divide
it into the numerator.

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So let's do that.

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93 goes into 13?

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Well, we know it goes
into 13 zero times.

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So let's add a
decimal point here.

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So how many times
does 93 go into 130?

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Well, it goes into it one time.

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1 times 93 is 93.

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Becomes a 10.

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That becomes a 2.

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

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Bring down a 0.

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So 93 goes into 370?

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Let's see.

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

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it only three times.

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3 times 3 is 9.

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3 times 9 is 27.

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So this equals?

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

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This become a 16.

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This becomes a 2.

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81.

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

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It goes roughly 8 times.

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

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

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good level of accuracy.

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

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

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

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decimal looks like.

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

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So let's write that down.

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And then finally, we have
this mixed number here.

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

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want to confuse you.

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

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

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

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that's less than 1.

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

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

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Actually, let's do it that way.

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Let's convert to an improper
fraction and then convert

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that into a decimal.

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

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clean up this a little bit.

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There.

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We have a little more
space to work with now.

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So 1 and 7/68.

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

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

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numerator here.

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And why does this make sense?

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

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

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

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module, as 68/68 plus 7/68.

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

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

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And now we convert this to a
decimal using the technique

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we did for 13/93.

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So we say-- let me
get some space.

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

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to run out of space.

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68 goes into 75 one time.

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1 times 68 is 68.

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75 minus 68 is 7.

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Bring down the 0.

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

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Ignore that decimal.

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68 goes into 70 one time.

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1 times 68 is 68.

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70 minus 68 is 2,
bring down another 0.

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68 goes into 20 zero times.

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

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already once again, gotten to
enough accuracy that

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we can compare.

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

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we kept dividing we'll keep
getting more decimals of

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

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

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So 35.7% is 0.357.

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

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that to do the work.

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It's 108.1% is equal to 1.081.

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0.5 is 0.5.

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13/93 is 0.138.

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

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So what's the smallest?

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

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The smallest is right here.

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

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So the smallest is 0.138.

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Then the next largest
is going to be 0.357.

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Then the next largest
is going to be 0.5.

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Then you're going to have 1.08.

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

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

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

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

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I always find it easier
to go into the decimal

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mode to compare.

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And actually, the hints
on the module will

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be the same for you.

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

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

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

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record some more videos with
more examples right now.

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Anyway, have fun.