[ale] [OT] Strange Request: Demonstrate a Calculator is Working Correctly

[Jay Lozier]

On 09/20/2015 09:37 AM, Tom Freeman wrote:
>
> I ran into a problem a while back, and I'm wondering if anybody has a 
> decent answer.
>
> Working at the board, I raced the students to get a calculation 
> performed. I shouldn't have bothered. Our respective results diverged 
> about the fourth place, with my little TI-30XA being a minority of 
> one. (Sadly, I didn't think to write the problem down for further 
> investigation.) I switched to a backup graphing calculator, and things 
> went smoothly.
>
> Question that some googleing hasn't properly answered: How do you test 
> a simple hand calculator to demonstrate proper operation?
>
> Obviously, the simple response is to dump the suspect calculator. 
> Trash it with extreme predjudice as it were.
>
> However, since there are individuals on this list who need extended 
> precision in their work, I wonder if they know how to test a hand 
> calculator for correctness.
>
> Come to think of it - having a faulty calculator or three and a 
> testing procedure might be a good instructional process for students. 
> We do need to trust our equipment, and we need to continuously check 
> it for error.
>
> In any event, my thanks to the list for the use of their bandwidth.

Interesting question.

I think the answer may be related to to big a word (IT definition) the 
calculator is using. Older calculators often used shorter words 
especially if they were cheap ones. They tend to have rounding errors 
relatively few decimals out.

There is an entire field of Numerical Methods/Analysis were people delve 
into this rather deeply into errors. There are three types: deliberate, 
bungles, and round-off. You are probably dealing with a round-off error 
caused by hardware/software limitations. A decent book on Numerical 
Methods will spend a chapter or so on round-off errors.

Jay

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