Anything other than powers of 1/2 (or their multiples) results in a form that repeats endlessly.

Not quite. Anything other than sums of powers of 2 result in a form that repeats endlessly.

Sums of powers of 2 do not repeat endlessly. For example, 0.3125 is not a power of 2, yet it does not repeat because it is a sum of powers of 2 (2-2 + 2-4).

Note that "powers of 1/2" and "powers of 2" are synonymous.

Update: Nevermind. What you said and what I said are mathematically equivalent. 0.3125 is a multiple of a power of 2 (5 * 2-4).

In reply to Re^2: adding numbers and floating point errors by ikegami
in thread adding numbers and floating point errors by smeenz

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