piclist 2001\05\30\130538a >
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : Barry Gershenfeld email (remove spam text)

We were taught: "Round off to make even".  It sounded outrageous
then and I'll admit to not doing it that way much.  But I think
the reasoning is sound.  Other posters have already said so.
Paraphrasing the example:
3.12471 = ?
3.12441 = ?
3.1245551 = ?
3.1245556 = ?

Nick Taylor said:
>You're right, it's not right.  Just drop the digits past the third
>decimal, then only consider the third decimal in your rounding.

Thus, in each example you consider just 3.124   =:-o

The premise is that since you are rounding to 3 digits, that the
4th digit is not reliable anyway (even though it looks like it
should be!)  Then, as David Gulley said:

>The idea here is that if you are tallying a series of values,
> the "random" nature of rounding some up, some down will
> "tend" to average out the errors.

And so they divide all possible digits into two groups:
0,2,4,6,8  and 1,3,5,7,9  .  So if digits occur randomly
then 50% of the time you round up and 50% of the time
you don't.

And in the example the answer is 3.124 no matter what
follows.

3.124x = 3.124
3.124xxxx = 3.124    (even if the x's are 9's  =:-o)

3.125x -> 3.126
3.126x -> 3.126
3.127x -> 3.128
3.128x -> 3.128   et c.

Well, I went to school in New Jersey :)  You wanted to know
what we were taught.  Take it or leave it. :)

Barry

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