Return to Video

Ordering numeric expressions

  • 0:00 - 0:04
    Welcome to the presentation on ordering numbers.
  • 0:04 - 0:06
    Lets get started with some problems that I think,
  • 0:06 - 0:08
    as you go through the examples hopefully,
  • 0:08 - 0:10
    you'll understand how to do these problems.
  • 0:10 - 0:12
    So let's see.
  • 0:12 - 0:14
    The first set of numbers that we have to order
  • 0:14 - 0:44
    is 35.7%,108.1%, 0.5, 13/93, and 1 and 7/68
  • 0:44 - 0:46
    So let's do this problem.
  • 0:46 - 0:48
    The important thing to remember whenever you're
  • 0:48 - 0:52
    doing this type of ordering of numbers is to realize
  • 0:52 - 0:55
    that these are all just different ways to represent
  • 0:55 - 0:59
    these are all a precent or a decimal or a fraction or
  • 0:59 - 1:02
    a mixed number--are all just different
    ways of representing numbers.
  • 1:02 - 1:05
    It's very hard to compare when
    you just look at it like this,
  • 1:05 - 1:07
    so what I like to do is I like to
    convert them all to decimals.
  • 1:07 - 1:12
    But, you know,there could be someone who
    likes to convert them all to percentages
  • 1:12 - 1:14
    or convert them all to fractions and then compare.
  • 1:14 - 1:17
    But I always find decimals to be
    the easiest way to compare.
  • 1:17 - 1:19
    So let's start with this 35.7%.
  • 1:19 - 1:22
    Let's turn this into a decimal.
  • 1:22 - 1:25
    Well, the easiest thing to remember is
    if you have a percent
  • 1:25 - 1:29
    you just get rid of the precent sign
    and put it over 100.
  • 1:29 - 1:38
    So 35.7% is the same thing as 35.7/100.
  • 1:38 - 1:41
    Like 5%, that's the same thing as 5/100
  • 1:42 - 1:45
    or 50% is just the same thing as 50/100.
  • 1:45 - 1:54
    So 35.7/100, well, that just equals 0.357.
  • 1:54 - 1:55
    If this got you a little confused
  • 1:55 - 1:59
    another way to think about percentage points is
    if I write 35.7%,
  • 1:59 - 2:03
    all you have to do is get rid of the percent sign
  • 2:03 - 2:07
    and move the decimal to the left two spaces
  • 2:07 - 2:10
    and it becomes 0.357
  • 2:10 - 2:12
    Let me give you a couple of
    more examples down here.
  • 2:12 - 2:14
    Let's say I had 5%.
  • 2:14 - 2:20
    That is the same thing as 5/100.
  • 2:20 - 2:22
    Or if you do the decimal technique, 5%,
  • 2:22 - 2:25
    you could just move the decimal
    and you get rid of the percent.
  • 2:25 - 2:29
    And you move the decimal over 1 and 2,
    and you put a 0 here.
  • 2:29 - 2:30
    It's 0.05.
  • 2:30 - 2:32
    And that's the same thing as 0.05.
  • 2:32 - 2:36
    You also know that 0.05 and
    5/100 are the same thing.
  • 2:36 - 2:38
    So let's get back to the problem.
  • 2:38 - 2:41
    I hope that distraction didn't distract you too much.
  • 2:41 - 2:43
    Scratch out all this.
  • 2:43 - 2:48
    So 35.7% is equal to 0.357.
  • 2:48 - 2:52
    Similarly, 108.1%.
  • 2:52 - 2:54
    Let's to the technique where
    we just get rid of the percent
  • 2:54 - 2:59
    and move the decimal space over
    1,2 spaces to the left.
  • 2:59 - 3:06
    So then that equals 1.081.
  • 3:06 - 3:11
    See we already know that this is samller than this.
  • 3:11 - 3:14
    Well the next one is easy,
    it's already in decimal form.
  • 3:14 - 3:16
    0.5 is just going to be equal to 0.5.
  • 3:16 - 3:21
    Now 13/93.
  • 3:21 - 3:24
    To convert a fraction into a decimal
  • 3:24 - 3:27
    we just take the denominator
    and divide it into the numerator.
  • 3:27 - 3:28
    So let's do that.
  • 3:28 - 3:34
    93 goes into 13?
  • 3:34 - 3:39
    Well, we know it goes into 13 zero times. Right?
  • 3:39 - 3:42
    So let's add a decimal point here.
  • 3:42 - 3:47
    So how many times does 93 go into 130?
  • 3:47 - 3:49
    Well, it goes into it one time.
  • 3:49 - 3:52
    1 times 93 is 93.
  • 3:52 - 3:56
    Becomes a 10.
  • 3:56 - 3:58
    That becomes a 2.
  • 3:58 - 4:02
    Then we're going to borrow, we get 37.
  • 4:02 - 4:05
    Bring down a 0.
  • 4:05 - 4:10
    So 93 goes into 370?
  • 4:10 - 4:11
    Let's see
  • 4:11 - 4:15
    4 times 93 would be 372, so it actually goes into
  • 4:15 - 4:16
    it only three times.
  • 4:16 - 4:22
    3 times 3 is 9.
  • 4:22 - 4:26
    3 times 9 is 27.
  • 4:26 - 4:31
    So this equals?
  • 4:31 - 4:37
    Let's see, this equals--if we say
    that this 0 becomes a 10.
  • 4:37 - 4:39
    This become a 16.
  • 4:39 - 4:41
    This becomes a 2.
  • 4:41 - 4:44
    81.
  • 4:44 - 4:48
    And then we say, how many times
    does 93 go into 810?
  • 4:48 - 4:50
    It goes roughly 8 times.
  • 4:50 - 4:52
    And we could actually keep going,
  • 4:52 - 4:54
    but for the sake of comparing these numbers,
  • 4:54 - 4:58
    we've already gotten to a
    pretty good level of accuracy.
  • 4:58 - 5:00
    So let's just stop this problem here
  • 5:00 - 5:01
    because the decimal numbers could keep going on,
  • 5:02 - 5:03
    but for the sake of comparison
  • 5:03 - 5:05
    I think we've already got a good
    sense of what this decimal looks like.
  • 5:05 - 5:10
    It's 0.138 and then it'll just keep going.
  • 5:10 - 5:12
    So let's write that down.
  • 5:12 - 5:15
    And then finally, we have this mixed number here.
  • 5:15 - 5:17
    And let me erase some of my work
  • 5:17 - 5:19
    because I don't want to confuse you.
  • 5:19 - 5:21
    Actually, let me keep it the way it is right now.
  • 5:21 - 5:22
    So these two ways
  • 5:22 - 5:25
    the easiest way to convert a
    mixed number into a decimal is
  • 5:25 - 5:30
    to just say, OK, this is 1 and then some fraction
  • 5:30 - 5:33
    that's less than 1.
  • 5:33 - 5:36
    Or we could convert it to a fraction,
    an improper fraction
  • 5:36 - 5:39
    like--oh, actually there are
    no improper fractions here.
  • 5:39 - 5:40
    Actually, let's do it that way.
  • 5:40 - 5:41
    Let's convert to an improper fraction
  • 5:41 - 5:42
    and then convert that into a decimal.
  • 5:42 - 5:46
    Actually, I think I'm going to need more space,
  • 5:46 - 5:49
    so let me clean up this a little bit.
  • 5:49 - 6:01
    There we have a little more space to work with now.
  • 6:01 - 6:08
    So 1 and 7/68.
  • 6:08 - 6:12
    So to go from a mixed number to
    an improper fraction,
  • 6:12 - 6:17
    what you do is you take the 68 times 1
  • 6:17 - 6:20
    and add it to the numerator here.
  • 6:20 - 6:21
    And why does this make sense?
  • 6:21 - 6:26
    Because this is the same thing as 1 plus 7/68. Right?
  • 6:26 - 6:29
    1 and 7/68 is the same thing as 1 plus 7/68.
  • 6:29 - 6:32
    And that's the same thing as you know
  • 6:32 - 6:39
    from the fractions module, as 68/68 plus 7/68.
  • 6:39 - 6:47
    And that's the same thing as 68 plus 7--75/68.
  • 6:47 - 6:52
    So 1 and 7/68 is equal to 75/68.
  • 6:52 - 6:54
    And now we convert this to a decimal
  • 6:54 - 6:56
    using the technique we did for 13/93.
  • 6:56 - 6:59
    So we say--let me get some space.
  • 6:59 - 7:04
    We say 68 goes into 75
  • 7:04 - 7:06
    suspicion I'm going to run out of space.
  • 7:06 - 7:09
    68 goes into 75 one time.
  • 7:09 - 7:13
    1 times 68 is 68.
  • 7:13 - 7:16
    75 minus 68 is 7.
  • 7:16 - 7:17
    Bring down the 0.
  • 7:17 - 7:20
    Actually, you don't have to write the decimal there.
  • 7:20 - 7:21
    Ignore that decimal.
  • 7:21 - 7:24
    68 goes into 70 one time.
  • 7:24 - 7:26
    1 times 68 is 68.
  • 7:26 - 7:30
    70 minus 68 is 2, bring down another 0.
  • 7:30 - 7:33
    68 goes into 20 zero times.
  • 7:33 - 7:35
    And the problem's going to keep going on,
  • 7:35 - 7:37
    but I think we've already once again,
  • 7:37 - 7:40
    gotten to enough accuracy that we can compare.
  • 7:40 - 7:47
    So 1 and 7/68 we've now figured out is equal to 1.10
  • 7:47 - 7:52
    and if we kept dividing we'll keep
    getting more decimals of accuracy,
  • 7:52 - 7:53
    but I think we're now ready to compare.
  • 7:53 - 7:56
    So all of these numbers I just
    rewrote them as decimals.
  • 7:56 - 8:00
    So 35.7% is 0.357.
  • 8:00 - 8:04
    108.1%--ignore this for now
  • 8:04 - 8:06
    because we just used that to do the work.
  • 8:06 - 8:09
    It's 108.1% is equal to 1.081.
  • 8:09 - 8:11
    0.5 is 0.5.
  • 8:11 - 8:15
    13/93 is 0.138.
  • 8:15 - 8:20
    And 1 and 7/68 is 1.10 and it'll keep going on.
  • 8:20 - 8:23
    So what's the samllest?
  • 8:23 - 8:25
    So the samllest is 0.
  • 8:25 - 8:27
    Actually, the smallest is right here.
  • 8:27 - 8:31
    So I'm going to rank them from samllest to largest.
  • 8:31 - 8:36
    So the samllest is 0.138.
  • 8:36 - 8:40
    Then the next largest is going to be 0.357. Right?
  • 8:40 - 8:43
    Then the next largest is going to be 0.5.
  • 8:43 - 8:46
    Then you're going to have 1.08.
  • 8:46 - 8:51
    And then you're going to have 1 and 7/68.
  • 8:51 - 8:56
    So hopefully, actually, I'm going to
    do more examples of this,
  • 8:57 - 9:00
    but for this video I think this
    is the only one I have time for.
  • 9:00 - 9:02
    But hopefully this gives you a
    sense of doing these problems.
  • 9:02 - 9:05
    I always find it easier to go into
    the decimal mode to compare.
  • 9:05 - 9:08
    And actually, the hints on the module
    will be the same for you.
  • 9:08 - 9:11
    But I think you're ready at least
    now to try the problems.
  • 9:11 - 9:12
    If you're not, if you want to see other examples,
  • 9:12 - 9:15
    you might just want to either re-watch this video
  • 9:15 - 9:20
    and/or I might record some more videos
    with more examples right now.
  • 9:20 -
    Anyway, have fun.
Title:
Ordering numeric expressions
Description:

Ordering numbers expressed as decimals, fractions, and percentages

more » « less
Video Language:
English
Duration:
09:22

English subtitles

Revisions Compare revisions