Dividing factorials on 15C CE

[Steve Simpkin]

(01-06-2024 07:23 PM)Johnh Wrote:  I get the same results on my 15C CE.

For a basically 40-year-old design, 15C's have plenty of calculation digits for any normal calculation, then or now. But these interesting cases are pushing the limits of the accuracy to which the final result can be delivered. We only notice this because we know that the true result of dividing two such factorials has to be a whole number, eg 50! / 45! = 46 x 47 x 48 x 49 x 50 = 254,251,200

I tried 50! / 45! with TouchRPN on my Samsung S22 using the HP15C mode and it did indeed deliver 254,251,200.0. But I'm assuming that although this App is generally a great emulation of the real thing it's not an exact digit for digit copy and it uses greater internal accuracy.

I think this also goes with the HP traditional philosophy of showing you the computed answer based on the number of significant digits stored by the hardware without using invisible "guard-digits" to round off the answer as TI and other calculator manufactures typically do.

There is some interesting history behind the decision on what to show the calculator user when the true result using fixed digit math is not what they expect to see. William Kahan had the following to say about the apparent "increased accuracy" of TI models when he worked as a consultant for HP.
This is discussed starting around page 144 on the following interview with Dr. William Kahan - August 2005
https://drive.google.com/file/d/1Jlg9EWQ...zwcol/edit