Converting Across Multiple Measurement Systems

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

2 thoughts on “Converting Across Multiple Measurement Systems

  1. Aaaaaaaaaaaaaaahhhhhhhhhhhhhhh, I know that voice! That is Prof. Alfaro <3! <3! Best math teacher in the history of EVER. <3

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