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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 [br]

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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 [br]

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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 [br]ways of representing numbers.

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It's very hard to compare when [br]you just look at it like this,

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so what I like to do is I like to [br]convert them all to decimals.[br]

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But, you know,there could be someone who [br]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 [br]the easiest way to compare.

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So let's start with this 35.7%.[br]

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Let's turn this into a decimal.

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Well, the easiest thing to remember is[br]if you have a percent

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you just get rid of the precent sign [br]and put it over 100.[br]

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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 [br]

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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 [br]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 [br]

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and it becomes 0.357

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Let me give you a couple of [br]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 [br]and you get rid of the percent.

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And you move the decimal over 1 and 2, [br]and you put a 0 here.[br]

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It's 0.05.

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And that's the same thing as 0.05.[br]

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You also know that 0.05 and[br]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.[br]

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So 35.7% is equal to 0.357.[br]

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Similarly, 108.1%.[br]

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Let's to the technique where [br]we just get rid of the percent

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and 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 this is samller 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 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 [br]and divide it into the numerator.

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So let's do that.

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93 goes into 13?[br]

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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[br]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[br]does 93 go into 810?

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It goes roughly 8 times.

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And we could actually keep going, [br]

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but for the sake of comparing these numbers,

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we've already gotten to a [br]pretty good level of accuracy.[br]

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So let's just stop this problem here [br]

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because the decimal numbers could keep going on,

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but for the sake of comparison[br]

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I think we've already got a good [br]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[br]

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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 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, [br]an improper fraction[br]

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like--oh, actually there are [br]no improper fractions here.[br]

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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[br]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.[br]

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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.[br]

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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.[br]

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So 1 and 7/68 is equal to 75/68.[br]

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And now we convert this to a decimal [br]

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using the technique we did for 13/93.[br]

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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.[br]

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68 goes into 75 one time.[br]

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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. [br]

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68 goes into 20 zero times.[br]

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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.[br]

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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 [br]getting more decimals of accuracy, [br]

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but I think we're now ready to compare.[br]

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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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108.1%--ignore this for now [br]

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because we just used that to do the work.[br]

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It's 108.1% is equal to 1.081.[br]

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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.[br]

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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.[br]

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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.[br]

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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.[br]

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Then you're going to have 1.08.[br]

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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 [br]do more examples of this,

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but for this video I think this[br]is the only one I have time for. [br]

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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 to go into [br]the decimal mode to compare.

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And actually, the hints on the module [br]will be the same for you.

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But I think you're ready at least [br]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 [br]with more examples right now.

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Anyway, have fun.