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Decimals to improper fractions program?
08-13-2018, 10:09 PM
Post: #22
RE: Decimals to improper fractions program?
(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:
+/- 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. ;-)

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RE: Decimals to improper fractions program? - Dieter - 08-13-2018 10:09 PM

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