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Another Simple Argument...

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Posted by Mark on November 27, 2001 16:38:57 UTC

What is the decimal representation of the fraction "one-third"?

1/3 = 0.33333333333333......

Now multiply both "1/3" and "0.333333" by the number 3, and notice the respective answers you get.

Both numbers are different representations of the same number correct? One is the rational quotient, or the "fraction" representation of the product obtained by multiplying the numbers 3 and 1/3. The other is the "decimal" expansion.

Therefore .99999999999...(ad infinitum) = 1
just as both products (1/3 * 3 and 3 * .333333...) are equal to 1.

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