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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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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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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