surrano@mailbox.hu (SZUCS Gábor) writes:
> As Tom pointed out, it isn't a floating point failure -- it is how rounding
> float is implemented. I assume anything with less than 15 digits can be
> exactly represented as float.
No, "decimal" fractions cannot ever be exactly represented in floating
point because since they use powers of two, you wind up with repeated
fractions.
1/3 is approximately 0.3333333, but you cannot present that exactly in
decimal.
In the very same way, 1/10 is approximately equal to
0.001001001001001001001001001001 (as a binary 'fraction'); the '001'
part is a repeating group, and wherever you terminate it, you lose
exactness.
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Christopher Browne
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