I'm curious whether some infinite periodic fractions in one counting system (e.g. decimal - 10/3 = 3.33333...) turn out to be non-infinite in another system and vice - versa.
Please excuse me if my terminology is not 100% accurate.
2026-03-29 07:36:37.1774769797
Are some infinite fractions in one counting system non-infinite in another?
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Yes.
$10_{10}/3 = 3 \frac{1}{3} = 10.1_3$, for instance.
Basically, if the denominator divides a sufficiently high power of the base, then the radix representation will terminate.
For example, $128|10^7$, so $\frac{1}{128_{10}}$ terminates in base 10 but continues forever in base 3.