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i hate to tell you, my friend, but you're wrong about the whole 1/3 thing. .3 repeating isn't irrational; it's rational because a rational number is defined as any number whose decimal repeats or terminates: 1/3 is exactly equal to .3 repeating, not a close approximation. if you take 1 and divide it by 3 (hence 1/3), you'll see that all you get is .33333...and so on. and as a side note, an irrational number is any number whose decimal component goes on, without terminating and without a distinguishable pattern, such as pi (3.1415...) or e (2.71...). so the whole .9 repeating = 1 is indeed true.
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