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Old 03-27-2008   #8
Infinite9
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I don't know how old this is, but here's my approach to the problem (apologies if bumping isn't allowed). Here, any number followed by an ellipsis ( … ) is recurring. Each line is numbered for the purpose of referring back to it (obviously)

1) 1/3 = 0.3…
2) 2/3 = 0.6…
3) 1/3 + 2/3 = 0.3… + 0.6…
4) 1/3 = 3/9 because 1/3 * 3/3 = 3/9
5) 2/3 = 6/9 because 2/3 * 3/3 = 6/9

6) 1/3 + 2/3 = 3/9 + 6/9 = 9/9 = 3/3 = 1/1 = 1
7) 0.3… + 0.6… = 0.9… = 1 because of line 3
8) 0.9… = 2/3 + 1/3 = 0.6… + 0.3… = 1