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 so rounding in passes is no worse than rounding in one go for this example.
vs.
3.46 -> 3
That was actually the debate with that teacher. Unbelievable as that still is to me today, she advocated the 3.46 -> 3.5 -> 4 route ...
I also know a didact which tells teachers that 1 has no prime decomposition. Oh, I see, she may have copied that from Wikipedia: http://en.wikipedia.org/wiki/Prime_factorisation