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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