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Cancelling / Converting Units: Examples (page 2 of 2)
A car's speedometer doesn't measure feet per second, so you'll have to convert to some other measurement. You choose miles per hour. You know the following conversions: 1 minute = 60 seconds, 60 minutes = 1 hour, and 5280 feet = 1 mile. If 1 minute equals 60 seconds (and it does), then The fact that the conversion can be stated in terms of "1", and that the conversion ratio equals "1" no matter which value is on top, is crucial to the process of cancelling units. We have a measurment in terms of feet per second; we need a measurement in terms of miles per hour. To convert, we start with the given value with its units (in this case, "feet over seconds") and set up our conversion ratios so that all undesired units are cancelled out, leaving us in the end with only the units we want. Here's what it looks like: Why did we set it up like this? Because, just like we can cancel duplicated factors when we multiply fractions, we can also cancel duplicated units: I would have to drive at 45 miles per hour. How did I know which way to put the ratios? How did I know which units went on top and which went underneath? I didn't. Instead, I started with the given measurement, wrote it down complete with its units, and then put one conversion ratio after another in line, so that whichever units I didn't want were eventually canceled out. If the units cancel correctly, then the numbers will take care of themselves. If, on the other hand, I had done something like, say, the following: ...then nothing would have cancelled, and I would not have gotten the correct answer. By making sure that the units cancelled correctly, I made sure that the numbers were set up correctly too, and I got the right answer. This "setting up so the units cancel" is a crucial aspect of this process.
For this, I take the conversion factor of 1 gallon = 3.785 liters. This gives me: = (6 × 3.785) liters = 22.71 L Since my bottle holds two liters, then: I should fill my bottle completely eleven times, and then once more to about onethird capacity. On the other hand, I might notice that the bottle also says "67.6 fl.oz.", right below where it says "2.0L". Since there are 128 fluid ounces in one (US) gallon, I might do the calculations like this: = 11.3609467456... bottles Copyright © Elizabeth Stapel 19992011 All Rights Reserved ...which, considering the roundoff errors in the conversion factors, compares favorably with the answer I got previously.
The conversion ratios are 1 acre = 43,560 ft^{2}, 1ft^{3} = 7.481 gallons, and five gallons = 1 water bottle. First I have to figure out the volume in one acrefoot. An acrefoot is the amount that it would take to cover one acre of land to a depth of one foot. How big is 0.86 acres, in terms of square feet? If I then cover this 37,461.6 ft^{2} area to a depth of one foot, this would give me 0.86 acrefeet of water, or (37,461.6 ft^{2})(1 ft deep) = 37,461.6 ft^{3} volume of water. But how many bottles does this equal? = 56,050.04592.... bottles ...or about 56,000 bottles every year. This works out to about 150 bottles a day. Can you imagine "living close to nature" and having to lug all that water in a bucket? Thank heaven for modern plumbing!
The conversion ratios are 1 wheelbarrow = 6 ft^{3} and 1 yd^{3} = 27 ft^{3}. Then I get: = 40,500 wheelbarrows Wow; 40,500 wheelbarrow loads! Even ignoring the fact the trucks drive faster than people can walk, it would require an amazing number of people just to move the loads those trucks carry. No wonder there weren't many of these big projects back in "the good old days"! When you get to physics or chemistry and have to do conversion problems, set them up as shown above. If, on the other hand, they just give you lots of information and ask for a certain resulting value, think of the units required by your resulting value, and, working backwards from that, line up the given information so that everything cancels off except what you need for your answer. For a table of common (and notsocommon) English unit conversions, look here. For metrics, try here. Here is another table of conversion factors. When I was looking for conversionfactor tables, I found mostly Javascript "cheetz" that do the conversion for you, which isn't much help in learning how to do the conversions yourself. But along with finding the above tables of conversion factors, I also found a table of currencies, a table of months in different calendars, the dots and dashes of Morse Code, how to tell time using ships' bells, and the Beaufort scale for wind speed. << Previous Top  1  2  Return to Index



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