Distribution of 0 digits in factorial series: Difference between revisions
Distribution of 0 digits in factorial series (view source)
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Because factorial numbers, which quickly become quite large, continue to have another terminal 0
on the right hand side of the number for every factor of 5
think that the proportion of zeros in a base 10 factorial number might be close to 1/5. However,
though the factorial products add another terminating 0 every
as the numbers become quite large, the number of digits in the factorial product expands exponentially,
and so the number above the terminating zeros tends toward 10% of each digit from 0 to 1
becomes larger. Thus, as the factorials become larger, the proportion of 0 digits in the factorial products
shifts slowly from around 1/5 toward 1/10, since the number of terminating zeros in n! increases only in
proportion to n, whereas the number of digits of n! in base 10 increases exponentially.
; The task:
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