Originally posted by: RossGr
Originally posted by: jagec
Originally posted by: RossGr
Once you start adding zeros in the long division problem there are only 23 possible remainders (0 - 22) so it is not possible to go more then 23 digits without repeating or terminating.
I don't think I understand what you're saying. Are you implying that doing long division by hand has a built-in maximum of 23 sig figs? How come? Or are you talking about calculators?
I am speaking about the the given problem, 8945/23. In ANY long division problem the denominator determines the max number of digits posssible before the quotent terminates or repeats. This is an application of what is known as the Pigeonhole property.
edit:
Actually Pigeonhole Principle on wiki.
I see...interesting. Hmm, what if you divide by an irrational number? Does this only hold true for integers, or for rational number, or for all numbers?
