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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,
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as you go through the examples,
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hopefully 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 is thirty-five point seven percent,
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one hundred eight point one percent, zero point five, thirteen over ninety-three, one, and seven over sixty-eight.
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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 of ordering of numbers
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is to realize that these are all just different ways to represent--
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these are all a percent or a decimal or a fraction or a mixed--
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are all just different 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 all to decimals.
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But 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 thirty-five point seven percent.
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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 percent sign and put it over one hundred.
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So thirty-five point seven percent is the same thing as thirty-five point seven over one hundred.
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Like five percent, that's the same thing as five over one hundred,
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or fifty percent is just the same thing as fifty over one hundred.
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So thirty-five point seven over one hundred, well, that[br]just equals zero point three five seven.
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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 thirty-five point seven percent,
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all you have to do is get rid of the percent sign and move the decimal to the left two spaces,
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and it becomes zero point three five seven.
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Let me give you a couple of more examples down here.
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Let's say I had five percent.
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That is the same thing as five over one hundred.
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Or if you do the decimal technique, five percent,
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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 one and two, and you put a zero here.
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It's zero point zero five.
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And that's the same thing as zero point zero five.
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You also know that zero point zero five and five over one hundred 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 thirty-five point seven percent is equal to zero point three five seven.
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Similarly, one hundred eight point one percent--
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Let's to the technique where we[br]just get rid of the percent and
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move the decimal space over[br]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[br]this is smaller than this.
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Well the next one is easy,[br]it's already in decimal form.
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0.5 is just going to[br]be equal to 0.5.
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[br]Now 13/93.
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To convert a fraction into[br]a decimal we just take the
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denominator and divide[br]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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[br]Well, we know it goes[br]into 13 zero times.
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So let's add a[br]decimal point here.
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So how many times[br]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[br]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,[br]so it actually goes into
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it only three times.
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[br]3 times 3 is 9.
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3 times 9 is 27.
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[br]So this equals?
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Let's see, this equals-- if we[br]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[br]times does 93 go into 810?
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It goes roughly 8 times.
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And we could actually keep[br]going, but for the sake of
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comparing these numbers, we've[br]already gotten to a pretty
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good level of accuracy.
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So let's just stop this problem[br]here because the decimal
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numbers could keep going on,[br]but for the sake of comparison
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I think we've already got a[br]good sense of what this
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decimal looks like.
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It's 0.138 and then[br]it'll just keep going.
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So let's write that down.
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And then finally, we have[br]this mixed number here.
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And let me erase some of[br]my work because I don't
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want to confuse you.
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Actually, let me keep it[br]the way it is right now.
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The easiest way to convert a[br]mixed number into a decimal is
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to just say, OK, this is 1[br]and then some fraction
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that's less than 1.
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Or we could convert it to a[br]fraction, an improper fraction
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like-- oh, actually there are[br]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[br]fraction and then convert
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that into a decimal.
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Actually, I think I'm going to[br]need more space, so let me
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clean up this a little bit.
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[br]There.
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We have a little more[br]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[br]an improper fraction, what you
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do is you take the 68 times 1[br]and add it to the
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numerator here.
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1 and 7/68 is the same[br]thing as 1 plus 7/68.
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And that's the same thing as[br]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[br]as 68 plus 7-- 75/68.
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So 1 and 7/68 is[br]equal to 75/68.
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And now we convert this to a[br]decimal using the technique
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we did for 13/93.
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So we say-- let me[br]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[br]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,[br]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[br]going on, but I think we've
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already once again, gotten to[br]enough accuracy that
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we can compare.
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So 1 and 7/68 we've now figured[br]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[br]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[br]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[br]from smallest to largest.
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So the smallest is 0.138.
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Then the next largest[br]is going to be 0.357. Right?
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Then the next largest[br]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[br]to have 1 and 7/68.
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Well, actually, I'm going to do[br]more examples of this, but for
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this video I think this is the[br]only one I have time for.
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But hopefully this gives you a[br]sense of doing these problems.
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I always find it easier[br]to go into the decimal
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mode to compare.
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And actually, the hints[br]on the module will
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be the same for you.
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But I think you're ready at[br]least now to try the problems.
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If you're not, if you want to[br]see other examples, you might
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just want to either re-watch[br]this video and/or I might
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record some more videos with[br]more examples right now.
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Anyway, have fun.