We’re converting between units of

measurement uh… we usually use these tables to help us out to help us

convert between the metric system which is used very frequently outside the

united states and the system that we use in the united states is on the right

over here So, usually we solve these problems using what we call dimensional analysis and heres a.. the best way to show

you an example of dimension analysis is just to do this problem here which says somebody kicked a ball for twelve meters. They want to know how

many be feet that is so the ball was kicked twelve meters What i want to happen is you can think of

these distractions and want meters to cancel with meters in the bottom and i want the final answer to be feet so and then i just need to find looking

at my table some conversion between feet and meters that will help and i have this first one right here tells me the one meter is three point two eight feet but i also have one at the bottom, the

one that says a zero point thirty meters is equivalent to about one foot so right now i’m going to focus on

this top one right here and in a minute, we’ll do an example using the bottom one and we’re going to get very similar answers so looking at the

top one, I know that one meter is equivalent to three point two eight

feet So when I’m doing dimensional analysis,

i’m going to go straight through and multiply this out twelve times three point twenty eight over one which is just twelve times three point

twenty eight that’s going to be a repeating decimal so the answers going to be approximately Sorry not a repeating decimal, just a regular decimal the final answers going to be something

like thirty nine point thirty six feet and round to two decimal places remember I said that we could also use the

bottom conversions, I’m going to do and example using the bottom conversion this time, we’re going to use that zero point thirty meters is about

one foot so we still start with the original twelve

meters we’re still doing dimensional analysis meters at the bottom feet in the top And you know according to my table using that Fact down at the bottom zero point thirty meters is about

equivalent to one foot So when we do dimensional analysis here, we’re going to

multiply the top members twelve meters times one foot is twelve the meters cancel and then the because the one down here

so the one times zero point thirty is zero point thirty We’re going to have to divide by twelve by

zero point thirty you divide twelve point zero point

thirty You get forty and this would be feet because it’s the only unit left over Remember our previous answer was thirty nine point thirty six feet so they’re not exactly equal with one another

uh… very close to and that happens because when we’re doing units conversions between different systems of measurement we’re usually using estimates See these squiggly lines here one here is approximately one point o_

nine yards, not exactly zero point thirty meters is approximately

one foot So that’s why you see those differencese in the answers

but they both just about right this is another example here If i drank two quarts of water they want to know how many liters that is so once again we’re going to have two quarts water I want to convert to liters, so I want quarts at

the bottom so they cancel and I want liters in the top this goes right here so they cancel correctly so we look at our chart, we need to locate conversions between quarts and liters here I have one one liter is approximately one point o

six quarts so the one point o six will go to the

bottom because that’s were quarts is and the one liter will go up top Then multiply this straight through and get two over one point o six. That’s telling me to divide when you divide two by one point o six you get approximately one point eight

eight liters, round two decimal places here something else you can do is you can also use the fact that zero point nine five liters is equivalent to one quart and then leave that as an exercise for you to

do you’re gonna get something very close to

one point eight eight: Remember the answers might not be exactly the same because of some rounding errors so for now you realize that this was a

very simple process regardless of what you’re trying to

convert Here, we’re trying to convert one thousand grams of sugar to ounces so I’m gonna set up my one thousand grams

of sugar and remember that i want grams of sugar on the

bottom and ounces on top so that the grams cancel each other out the next part is just to look at my

table for some sort of conversion between grams and ounces and i’m looking here and I see twenty eight point thirty five

grams is about one ounce that’s a fact i’m going to use, so the one ounce

goes on top because thats where ounces is the twenty eight point thirty five grams goes on the bottom, that’s where

the g is multiply this through, you get one

thousand grams over twenty eight point thirty five that’s going to be a division when I divide one thousand by twenty eight point

point thirty five you get approximately thirty five point twenty-seven that’s going to be in ounces because of what we want to convert to and we have one last example in this example, you want to convert

celsius thirty-seven degrees celsius to an unknown temperature in fahrenheit so this is a little bit different: we can’t really

do temperature to do dimensional analysis because it turns out that temperature in

celsius and temperature in farenheit is not an exact conversion we can’t just boil it down to one number that

represents another number and a different number, so we have to use the

formula in this case we want to convert to degrees

fahrenheit so I’m going to use this formula here whenever you want it convert to degrees

celsius, you would use the other formula so the formula tells me that whatever the

degrees fahrenheit is, its going to be nine fifths the degrees celsius was thirty two so i know how many degrees celsius it is

because it was given in the problem, it was thirty seven degrees celsius and to do this, I’m going to multiply nine fifths by

thirty seven you can do that with any number of ways you can convert nine fifths to a decimal, multiply it by thirty seven or take nine times seven, divide that by five Either way you do it you’re going to get sixty six point six You want to add that to thirty two to get the final answer which is going to be ninety eight point six degrees fahrentheit I did a little rounding here, so really i should stop using these equal signs As soon as you start rounding, you should use the

squiggly lines because that means that it’s approximately equal to

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