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# Ordering numeric expressions

## Video transcript

welcome to the presentation on ordering numbers let's get started with some problems and I think as we go through the examples hopefully you'll understand how to do these problems so let's see the first set of numbers that we have to order is 35.7% 108 0.1% 0.5 13 over 93 and 1 and 7/68 so let's do this wrong so the important thing to remember whenever you're doing this type of ordering ordering of numbers is to realize that these are all just different ways to represent these are all a percent or a decimal or a fraction or mixed numbers are all just different ways of representing numbers and it's very hard to compare when you just look at it like this so what I like to do is I like to convert them all to decimals but you know there could be someone who likes to convert them all to percentages or convert them all to fractions and then compare but I always find decimals to be the easiest way to compare so let's start with this 35.7% let's turn this into a decimal well the easiest thing to remember is if you have a percent you just get rid of the percent sign and put it over 100 so thirty five point seven percent is the same thing as thirty five point seven over 100 like five percent that's the same thing as 5 over 100 or 50 percent is just the same thing as 50 over 100 so thirty five point seven over 100 well that just equals 0.357 if this got a little confusing another way to think about percentage points is if if I write thirty five point seven percent all you have to do is get rid of the percent sign and move the decimal to the left two spaces and it becomes point three five seven let me give you a couple of more examples down here let's say I had five percent that is the same thing as five over 100 or if you do the decimal technique 5% you could just move the decimal you get rid of the percent and you move the decimal over one and two when you put a zero here it's a point oh five and that's the same thing as 0.05 and you also know that 0.05 and 500 the same thing so let's get back to the problem I hope I didn't that distraction didn't distract it too much let me scratch out all this so 35.7% is equal to 0.35 seven similarly one hundred and eight point one percent let's do the technique where we just get rid of the percent and move the decimal space over one two spaces to the left so then that equals 1.08 one so we already know that this is smaller than this well the next one is easy it's already in decimal form 0.5 is just going to be equal to 0.5 now 13 over 93 to convert a fraction into the debt into a decimal we just take the denominator and divide it into the numerator so let's do that 93 goes into 13 goes into 13 well we know it goes into 13 zero times right so let's add a decimal point here so how many times is 93 go into 130 well it goes into it one time one times 93 is 93 comes the 10 that becomes a 2 later we're going to borrow since we get 37 bring down a zero so 93 goes into three hundred and seventy I think it's C Ford times 93 would be 360 it'd be three instead of two so actually goes into only three times three times three times three is nine 3 times 9 is 27 27 so this equals C this equals if we say that this 0 comes a 10 this becomes 16 this comes to 81 let me say how many times since 93 goes into 810 it goes roughly 8 times and we could actually keep going but for the sake of comparing these numbers we've already gotten to a pretty good level of accuracy so let's just let's just stop this problem here because the decimal numbers could keep going on but for the sake of comparison I think we've already got a good sense of what this decimal looks like it's one point 1 3 8 and then it'll just keep going so let's write that down and then finally we have this mixed number here and let me erase some of my work because I don't want to confuse you actually let me keep it the way it is right now so there's two ways the easiest way to convert a mixed number into a decimal is to just say okay this is 1 and then some fraction that's less that's that's less than 1 or we could convert it to a fraction an improper fraction like actually there are no improper fractions here but let's actually let's do it that way let's convert to an improper fraction and then convert that into a decimal so 1 and actually I think I'm going to need more space so let me clean up this a little bit dum de dum de dum dum dum de dum de dum de dum de dum dum there there I can have a little more space to work with now so 1 and 7/68 so to go from a mixed number to an improper fraction what you do is you take the 68 times 1 and add it to the numerator here and why does this make sense because this is the same thing as 1 plus 7 over 68 right one in 768 is the same thing as 1 plus 7 over 68 and that's the same thing as you know from the fractions module a 68 what 68 over 68 plus 7 over 68 and that's the same thing as 68 plus 7 is 75 over 68 so one in 768 is equal to 75 or 68 and now we convert this to a decimal using the technique we did 413 over 93 so we say let me get some space so we say 68 goes into 75 suspicion I'm going to run out of space with 68 goes into 75 one time one times 68 68 75-68 seven bring down the 0 I actually don't have to write the decimal there 68 goes into ignoring the decimal 68 goes into 70 one time one times 68 is 68 70 minus 68 is to bring down another zero 68 goes into 20 zero times and the problems going to keep going on so but we can I think we've already once again gotten to enough accuracy that we can compare so one in seven 68 we've now figured out is equal to one point one zero and if we kept dividing we'll keep getting more decimals of accuracy but I think we're now ready to compare so all of these numbers I just rewrote them as decimals so 35.7% is 0.35 seven one hundred and eight point one percent and ignore this for now because we just use that to do the work it's one hundred and eight point one percent is equal to 1.0 eight 10.5 is 0.5 13 over 93 is 0.138 and 1 and 7/68 is one point one zero and it will keep going on so what's the smallest so the smallest is point actually no the smallest is right here so this is I'm going to rank them from smallest to largest so the smallest is 0.138 then the next largest is going to be 0.357 right then the next largest is going to be 0.5 then you're going to have one point oh eight and then you're going to have 1 and 7/68 so hopefully well actually I'm going to do more examples of this but for this video I think I think this is the only one I have time for but hopefully this gives you a sense of doing these problems I always find it easier to go into the decimal mode to compare and actually the hints on the module do the same for you but I think you're ready at least now to try the problems if you're not if you want to see other examples you might just want to either re watch this video and or I might record some more videos with more examples right now anyway have fun