## 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,
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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,
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point five,
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thirteen over ninety-three,
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and one and seven sixty-eighths.
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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 mixed numbers--
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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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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
just equals 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 point three five seven.
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Let me give you a couple 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 point zero five.
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And that's the same thing as point zero five.
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You also know that 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 point three five seven.
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Similarly, one hundred eight point one percent--
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Let's do the technique where we
just get rid of the percent
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and move the decimal space over one, two spaces to the left.
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So then that equals one point zero eight one.
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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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Point five is just going to be equal to point five.
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Now thirteen over ninety-three.
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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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Ninety-three goes into thirteen?
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Well, we know it goes into thirteen zero times.
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So let's add a decimal point here.
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So how many times does ninety-three go into one hundred thirty?
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Well, it goes into it one time.
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One times ninety-three is ninety-three.
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Becomes a ten.
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That becomes a two.
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Then we're going to borrow, so get thirty-seven.
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Bring down a zero.
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So ninety-three goes into three hundred seventy?
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Let's see.
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Four times ninety-three would be three hundred seventy-two,
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so it actually goes into it only three times.
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Three times three is nine.
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Three times nine is twenty-seven.
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So this equals?
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Let's see, this equals-- if we say that this zero becomes a ten.
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This become a sixteen.
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This becomes a two.
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Eighty-one.
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And then we say, how many times does ninety-three go into eight hundred ten?
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It goes roughly eight 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 point one three eight 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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The easiest way to convert a mixed number into a decimal is to just say,
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okay, this is one and then some fraction that's less than one.
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Or we could convert it to a fraction, an improper fraction like--
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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.
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We have a little more space to work with now.
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So one and seven sixty-eighths.
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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 sixty-eight times one
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and add it to the numerator here.
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Why does this make sense?
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Because this is the same thing as one plus seven over sixty-eight.
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One and seven sixty-eighths is the same thing as one plus seven over sixty-eight.
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And that's the same thing, as you know from the fractions module,
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as sixty-eight over sixty-eight plus seven over sixty-eight.
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And that's the same thing as sixty-eight plus seven-- seventy-five-- over sixty-eight.
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So one and seven sixty-eighths is
equal to seventy-five over sixty-eight.
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And now we convert this to a decimal
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using the technique we did for thirteen over ninety-three.
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So we say-- let me get some space.
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Sixty-eight goes into seventy-five one time.
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One times sixty-eight is sixty-eight.
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Seventy-five minus sixty-eight is seven.
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Bring down the zero.
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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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Sixty-eight goes into seventy one time.
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One times sixty-eight is sixty-eight.
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Seventy minus sixty-eight is two, bring down another zero.
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Sixty-eight goes into twenty 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 one and seven sixty-eighths, we've now figured out, is equal to one point one zero--
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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 thirty-five point seven percent is point three five seven.
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One hundred eight point one percent is equal to one point zero eight one.
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Point five is point five.
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Thirteen over ninety-three is point one three eight.
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And one and seven sixty-eighths is one point one zero 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 point one three eight.
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Then the next largest is going to be point three five seven. Right?
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Then the next largest is going to be point five.
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Then you're going to have one point zero eight.
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And then you're going to have one and seven sixty-eighths.
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Well, 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 do 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 either 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
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