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Gamo · (This post was last modified: 08-14-2018 01:36 AM by Gamo.)

Found this on HP Newsletter issue #25

Decimal to Fraction for the HP-35S by Joseph K. Horn

On Page 35

http://h20331.www2.hp.com/hpsub/download...r_2011.pdf

Gamo

Dieter · 08-13-2018, 10:09 PM

(08-13-2018 03:03 AM)Albert Chan Wrote:
(06-09-2018 02:54 PM)Csaba Tizedes Wrote: In engineering practice more important the relative error. In this case the results are:

Code:

+/- 1.000% error: 19/6, +/- 0.100% error: 22/7, +/- 0.010% error: 289/92, +/- 0.001% error: 355/113

Above table is mistaken, 355/113 is 100 times more accurate.
355/113 vs Pi, relative error = 85e-9 = 0.0000085%

I think the idea of the table is to give a fraction that – at least – matches a certain accuracy level. So if you need an accuracy of 0,001% or better, 355/113 is the first fraction to meet that target.

(08-13-2018 03:03 AM)Albert Chan Wrote: I agree that relative error is more useful than digits matched.
All estimates below had 5% relative error, but digits matched are all over the place.

That's exactly why I prefer stating the number of matching digits.
But I am not an engineer. ;-)

Dieter