On Mon, 27 Oct 2008, Daniel Fischer wrote:
Am Montag, 27. Oktober 2008 11:46 schrieb Henning Thielemann:
On Mon, 27 Oct 2008, Janis Voigtlaender wrote:
Henning Thielemann wrote:
I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then
0.45 - (round to one place) -> 0.5 - (round to integer) -> 1
But repeated rounding *is* worse than rounding in one go, under any reasonable scheme:
3.46 -> 3.5 -> 4
With the rounding-to-even route this would be
3.46 -> 3.4 -> 3
Wait, that cannot be. 6 > 5, so 3.46 -> 3.5 even with banker's rounding.
You are right, my oversight. So only the method helps, that the last digit is marked, whether it was generated by rounding up or down.