Casio rounding

[Pekis]

Hello,

I found this in the Casio FX-602P manual:
What do you think of it ? I Wonder if it's specific to that model ...

[Albert Chan]

It is nice to see how well old manual does things.
Nowadays, this rounding stuff have to discover by yourself ...

Casio FX-115MS: 1E11 + 1 - 1E11 => 0, 1E11 - 1 - 1E11 => 0
Casio FX-3650P : 1E11 + 1 - 1E11 => 0, 1E11 - 1 - 1E11 => -1

Both Casio had a display bug:

e => 2.718281828
Ans÷10 => 0.271828182
Ans÷10 => 0.027182818
Ans÷10 => 2.718281828e-03

[Eddie W. Shore]

Interesting. The rounding scheme seems to be has been arbitrarily chosen instead of going with the traditional rule of looking at the last digit and rounding up when it is 5 or more.

[toml_12953]

(11-14-2018 01:59 PM)Eddie W. Shore Wrote:  Interesting. The rounding scheme seems to be has been arbitrarily chosen instead of going with the traditional rule of looking at the last digit and rounding up when it is 5 or more.

For statistics, the rule is round to the nearest even digit:

Round to one decimal place:
5.55 ==> 5.6
5.45 ==> 5.4

[ijabbott]

(11-14-2018 01:59 PM)Eddie W. Shore Wrote:  Interesting. The rounding scheme seems to be has been arbitrarily chosen instead of going with the traditional rule of looking at the last digit and rounding up when it is 5 or more.

I think it's just the usual trick that some calculators do to "correct" small round-off errors instead of leaving them alone. However, these "corrections" can make the result worse. For example, 920/99 would produce an internal answer of 9.29292929292 or 9.29292929293 which the FX-602P would round off internally to 9.29292929300 before any subsequent operations were performed on it. (I haven't tested this on an actual FX-602P.)

[Eddie W. Shore]

(11-14-2018 03:39 PM)toml_12953 Wrote:  

(11-14-2018 01:59 PM)Eddie W. Shore Wrote:  Interesting. The rounding scheme seems to be has been arbitrarily chosen instead of going with the traditional rule of looking at the last digit and rounding up when it is 5 or more.

For statistics, the rule is round to the nearest even digit:

Round to one decimal place:
5.55 ==> 5.6
5.45 ==> 5.4

I don't think I was familiar with this method (Banker's method if I recall correctly) until Richard Nelson's talk about rounding methods at HHC 2018.

[toml_12953]

(11-19-2018 01:46 PM)Eddie W. Shore Wrote:  

(11-14-2018 03:39 PM)toml_12953 Wrote:  For statistics, the rule is round to the nearest even digit:

Round to one decimal place:
5.55 ==> 5.6
5.45 ==> 5.4

I don't think I was familiar with this method (Banker's method if I recall correctly) until Richard Nelson's talk about rounding methods at HHC 2018.

I think it's popular with statisticians since it tends to reduce rounding error when given a large sample population.