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Ordering numeric expressions

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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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    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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    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 we kept dividing we'd get more decimals of accuracy. So we're 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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    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 . -- 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. Right?
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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.
Title:
Ordering numeric expressions
Description:

Ordering numbers expressed as decimals, fractions, and percentages

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Video Language:
English
Duration:
09:22

English subtitles

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