Approximate pi to 24 digits via keyboard

[Rick314]

(02-01-2015 07:24 PM)Thomas Klemm Wrote:  

(02-01-2015 05:34 PM)Dieter Wrote:  So should the calculator drop the last four digits and return 3,9569936 E+435 for e¹⁰⁰³ instead?

After all you should take the result with a grain of salt. The relative error is multiplied by 1003 thus the last 3-4 digits are indeed meaningless. But at least the first 8 digits are significant.

Hello Thomas. I'm with Dieter here, and yes absolutely non-entered input digits should be considered to be 0. e^1003, e^(1003 + 1e-8) and e^(1003 - 1e-8) are distinct different recognizable inputs to a 12-digit calculator and each has a different unique 12-digit approximation to the exact correct answer. (I checked with extended-precision software and Dieter's 3 answers are indeed the best 12-digit answers possible. They are also what my HP-35S returns, so kudos to the HP-35S same as for its sin(x) algorithm.) I don't think there is any "relative error" on the 3 different inputs, and the 3 different answers are the correct 12-digit answers.