Finding Areas using Unit Conversions
Date: 3/19/96 at 1:38:33 From: Heikki Jokipii Subject: Too simple a question Dear Dr. Math, I am not an American and I am not a child in the American elementary school - and that is exactly the reason why I write this letter. I am interested in the following problem which is presumably very elementary for you, but I can not find an answer to it here in Finland where I live - I simply can't find your elementary school text-books in math here. It is so elementary that I could not find anything of it in your archives, either. As you surely know, we in Europe use the metric system. In the metric system, calculating an area of a rectangle is very simple: just one multiplication and there it is. If you then want to express the result, say, in centimeters instead of kilometers, you only have to move the decimal point. But how do you use to count the area, expressed in your traditional units. For example: how do you calculate the area of a rectangle, where one side is, say, 2 miles, 3 furlongs, 4 yards, 2 feet and 5 inches and the other, say, 1 mile, 7 furlongs, 47 yards, 1 feet and 11 inches? The result in acres and so on? I can solve this problem, of course, in my way. But there have to be a way that is more systematic and I know that there is: the way you Americans (and English) use. To be more exact: I mean the way you do the calculation(s) with pencil and paper. If you kindly would describe me this systematic calculating method I would be very grateful. Yours Heikki Jokipii
Date: 3/19/96 at 13:14:5 From: Doctor Aaron Subject: Re: Too simple a question This type of a calculation is a pain with English units because unlike metric units they don't have a natural decimal representation. Eventually we will have to write the area as a decimal or use inconvenient units like square inches or absurd units like inches*miles. One way to do it is to convert everything to inches, multiply, and reconvert into square miles. 2 feet = 24 inches. 4 yards = 12 feet = 144 inches. 3 furlongs = 1980 feet = 23,760 inches. 2 miles = 10,560 feet = 126,720 inches. So 2 miles + 3 furlongs + 4 yards + 2 feet + 5 inches = 150,653 inches. Similarly, 1 mile + 7 furlongs + 47 yards + 1 feet + 11 inches = 120,515 inches. To get the area, we just multiply the sides (hopefully with a calculator) to get 18,155,846,295 square inches. Since there are 4,014,489,600 square in a square mile (5280feet/mile * 12 inches/foot)^2, we can divide to get 4.522 square miles. We could've also converted to miles before the multiplication to avoid dealing with such big numbers. Then 150,653 inches = 2.377 miles, and 120,515 inches = 1.902 miles, so the area of the rectangle spanned by these two sides will be 2.377*1.902 = 4.521 square miles. There is a rounding error in the last decimal place, but the two answers basically agree with each other. I think that the tediousness of this seemingly simple calculation illustrates the ease of working with the metric system. -Doctor Aaron, The Math Forum
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