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    The Significant Figures Thing
    From: David Pike
    Date: 2014 Dec 25, 02:12 -0800

     

    I’ve been thinking about this “places of decimals” thing.  I seem to remember a rule in science and engineering that says “Try and minimise the number of values which are already worked out figures in themselves you use to calculate the value your looking for” or something like that.  Unfortunately, in spherical and ellipsoidal trigonometry formulas, there are situations where a tiny change in one of the input values makes a big difference in the final answer.  This was why, before the days of calculators and computers, navigators used a minimum of five figure tables and often six or seven figure tables.  http://www.jstor.org/discover/10.2307/3610849?sid=21104932187381&uid=2&uid=3738032&uid=70&uid=4&uid=2129 I remember in about 1974, when HP scientific calculators (about the size of a small suitcase, and you had to book time on it) were becoming available at great cost, seeing that someone at RAF Manby, the home of RAF Specialist Navigation at the time, had thrown a beautifully bound set of six, or was it seven, figure tables into a dustbin and thinking “Perhaps I should rescue those.  They might be valuable one day”.  But of course, I never did.  So use as many places of decimals as possible during your calculations, but don’t expect the guy on the ground to apply your final answer to that level of accuracy.  Dave

     

       
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