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Ordering numeric expressions

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    Welcome to the presentation on ordering numbers.
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    Lets get started with some problems that I think,
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    as you go through the examples hopefully,
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    you'll understand 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
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    is 35.7%,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
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    doing this type of ordering of numbers is to realize
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    that these are all just different ways to represent
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    these are all a precent or a decimal or a fraction or
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    a mixed number--are all just different ways of representing numbers.
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    It's very hared 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 all to decimals.
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    But, you know,there could be someone who likes to convert them all to percentages
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    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 percent
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    you just get rid of the precent sign and 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
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    or 50% is just 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
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    another way to think about percentage points is if I write 35.7%,
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    all you have to do is get rid of the percent sign
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    and move the decimal to the left two spaces
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    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%,
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    you could just 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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    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
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    and 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 samller 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
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    we just take the 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. Right?
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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, we 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,
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    but for the sake of comparing these numbers,
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    we've already gotten to a pretty good level of accuracy.
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    So let's just stop this problem here
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    because the decimal numbers could keep going on,
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    but for the sake of comparison
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    I think we've already got a good sense of what this 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
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    because I don't want to confuse you.
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    Actually, let me keep it the way it is right now.
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    So these two ways
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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
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    and then convert that into a decimal.
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    Actually, I think I'm going to need more space,
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    so let me clean up this a little bit.
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    There 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,
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    what you do is you take the 68 times 1
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    and add it to the 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. Right?
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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
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    from the fractions 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
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    using the technique 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
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    suspicion I'm going 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,
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    but I think we've already once again,
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    gotten to enough accuracy that we can compare.
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    So 1 and 7/68 we've now figured out is equal to 1.10
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    and if we kept dividing we'll keep getting more decimals of accuracy,
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    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
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    because we just used 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 samllest?
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    So the samllest is 0.
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    Actually, the smallest is right here.
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    So I'm going to rank them from samllest to largest.
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    So the samllest 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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    So hopefully, actually, I'm going to do more examples of this,
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    but for 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 mode to compare.
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    And actually, the hints on the module will 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,
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    you might just want to eithere re-watch this video
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    and/or I might 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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