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math problem debate
(15 posts)
Jack, the notation 0.333... is a mathematical shortcut for writing in decimal a fraction that has an infinite number of decimal places. You read it as, "point 3, 3, 3 repeating forever". If you continue to work with fractions, it's quite clear that:
1/3 * 3 = 1
This is read as "one third times three equals one." It is not as obvious in decimal, but it's still true that:
.333... * 3.0 = 1.0
Reading, "point 3, 3, 3, repeating forever times three point zero equals one point zero". It's just hard to wrap your head around an infinitely repeating decimal.
EDIT: proof of this is left to the reader. Also, check your calculator because it knows the answer as well.
Lighthouse, repeating, recurring. I guess we will have to agree to be separated by a common language. :)
Jack, while looking up "repeating decimal" at wikipedia, I saw that they have a special discussion on 0.999... including a proof that it's equal to 1. Check this math out folks:
http://en.wikipedia.org/wiki/R.....0.99999...
People can be irrational, life can be irrational, now you are telling me that numbers can be irrational? Is there no sanity in the world?!? :-)
Pi and the square root of 2 (2 ^ .5) are irrational numbers because they cannot be represented by the fraction of two integers. The fraction 1/3 is certainly a rational number, as is .333... because it can be represented as a rational. From Wikipedia: "The decimal expansion of an irrational number never repeats....":
http://en.wikipedia.org/wiki/I.....expansions
"Math class is tough. Let's go shopping!" -- Barbie Doll
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