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+--- Thread: Decimals to improper fractions program? (/thread-10873.html)
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RE: Decimals to improper fractions program? - Gamo - 08-13-2018 01:01 PM
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/downloads/HP_Calculator_eNL_09_September_2011.pdf
Gamo
RE: Decimals to improper fractions program? - 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