Monday, October 6, 2008
The Accuracy of 8-Digit Calculators
I just finished my last chemistry problem for this week's homework: find Avagadro's number using blah-blah-blah data about an 8-atom silicon cube. I wanted to get A's # as accurately as I could, so I decided to do the whole thing by hand. I thought, "My calculator can only work with 8 digits, so I'll do this with a pencil, take up a whole page, and get the answer as precise as possible!" The first step was converting X picometers to X centimeters cubed. When I finished multiplying 12-digit numbers, I went to the back of the book to check on my progress, get an idea of where I should be, and use the rounded numbers in the back of the book to see how precise the book's answer would be. I saw that I was 0.04 x 10 -22 off, but I figured that it was due to my superior decimal places. Wrong-o. My final calculation came to 6.10etc. instead of 6.02etc. I realized that my quantity of 0.000000000000000000000158151477991 cm3 was worse than a rounded 0.0000000000000000000001602 cm3. The extra precision I shot for was lost, probably to a single mistake, within the 12-digit multiplications that took me so long. Go figure.
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2 comments:
I had that exact problem with my own calculator, in chem... I finally made myself a little chart to work around the problem. I don't remember what I ended up doing, but it worked. Pretty sad, when you have to help a calculator... ^_^
A fellow classmate from physical science last year had a very unreliable calculator. In between classes he turned it on and pressed "=" and it gave him "666" out of nowhere. We made sure we informed our literature teacher that his calculator was possessed. = )
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