in reply to RE: Methods to format a number
in thread Numbers....

While this method is quite slick, it won't work as expected with numbers that are of the form 0.5, as it will always round up to the next number instead of rounding to the nearest even number (a rule which tries to make sure that most rounding errors cancel each other).

Update: nuance has updated the above post, so this post has become meaningless ;).

Here is an example for a case when always rounding up and using the results in further calculation. Adam calls this "premature rounding", but I think there are valid cases to do this, for example when doing accounting or printing invoices. In this example, using the rounded values in further calculations increases the error introduced by rounding :
Consider (for simplicity) 2.5 * 3.5 :
MethodResultError
exact8.750
round up12.003.25
round to nearest even number8.000.75
In this (extreme) example, the rounding errors don't cancel each other out when always rounding up. There are also cases where rounding up and rounding to the nearest even number give the same rounding error (consider 3.5 * 1.5).

And by the way, I'm not pedantic, I'm just trying to be accurate :)

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RE: RE: RE: Methods to format a number
by Adam (Vicar) on Jun 02, 2000 at 21:07 UTC
    You know, I love this web site! Why? Because I am always learning something. Usually its about Perl, but today it was about rounding.

    Corion's post confused me greatly because I had never heard of rounding to the nearest even... so I cruised out onto the internet and discovered a plethora of sites (mostly in college math departments) that defend it! So I am swayed. I also found an interesting site about significant digits.

    So, thank you Corion! You have my vote.