Calculator Related Math/Science Fair Project


The manger of the calculator group came to me today asking for some help/suggestions on something, and I think this is something that may be of some interest here. I know for sure I could definitely use some help.

Basically, his 8th grade daughter wants to do a project examining calculator precision and accuracy with various types of calculations. They are looking at both finance and scientific type calculations and trying to figure out how to test and compare this between different models. In addition, how this can help determine possible methods used to perform the calculations internally.

I know there have been a lot of discussions here in the past on calculator forensics, but I am not as familiar with them as I'd like.

Basically, I am hoping I can get some suggestions on:

1. Which forensics will be most interesting?

2. Which units should would be most interesting?

3. How and what would be good tests for financial calculations that would be interesting?

4. Any relevant links that could be helpful.

5. Any information or suggestions on how a project like this could be exciting and engaging for an 8th grade (~13yrs old students) advanced science/math class

I was planning to pass this post along to them for review, so feel free to post here and discuss. Thanks in advance.


Edited: 29 Oct 2010, 2:42 p.m.


I think it was Joe Horn who posted a very simple way to tell if a calculator is doing binary or decimal arithmetic, and to get an idea of the precision. Enter 1/3 into the calculator. Then subtract the most significant digits. Repeat the process. If it's doing decimal, the digits will go to zero in some "sane" way. If binary then it will start to look strange.

For an 8th grader, the project could be "how to calculators calculate." It could talk about the fact that they use base 10 instead of base 2 like computers, and the fact that they use scientific notation. She could talk a little about BCD arithmetic and maybe the fact that calculators can REALLY only do addition, subtraction and maybe multiplication. All the other operations are done with these and clever algorithms. She might talk about one of those algorithms, like the square root, or 1/x and the fact that calculators divide by multiplying by 1/x (I assume that's the way it's done).




a very good introduction to errors in numerical calculations can be found in

Peter Henrici

Essentials of Numerical Analysis (with Pocket Calculator Demonstrations), 1982

You will get the book second hand for a few dollars at The book comes with many calculator demonstration, using HP 33 or 34, covering rounding errors, error propagation, the lot.

E.g. solving x^2-1634 x+2=0 teaches something about cancellation. That would be accessible for an 8th grader.

On the web: has a test suite for numerical experiments.

Hugh Steer has some nice tests at




Here are some references:

1. Mike Sebastian's Calculator Forensics at

2. The old Paranoia programs which would find Radix, Precision, guard digit or not, etc. See "Paranoia: A Floating Point Benchmark" by Richard Karpinski on pages 223-235 of the February 1985 issue of BYTE. You can see the application to a number of different machines at V10N2P16ff of TI PPC Notes which is available at Viktor Toth's site.

3. There were some benchmarks published in Scientific American in the 1980's. If you can't find them let me know and I will have to do a little searching.

4. Somewhere in this forum there is a simple test test by Rodger Rosenbaum.

5. Kahan's Mathematics Written in Sand

6. How about discussing potential problems due to the four level RPM stack or the limit on pending operations in algebraic systems?

7. The HP-15C Advanced Functions Handbook has some good examples including a series of tests to define the quality of a quadratic solution.


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