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Re: M.O.A. to Degrees wondering
From: Paul Hirose
Date: 2022 Aug 6, 14:46 -0700

On 8/6/2022 10:30 AM, Herman Dekker wrote: > I wondered why the conversion of minutes of arc to degrees, mostly gaves > values with a repetitive figure. That happens because a fraction does not convert to a terminating decimal unless the denominator (after the fraction is "reduced") has prime factors of 2 and 5 only. For example, 1/60 does not terminate because 60 = 2 * 2 * 3 * 5. But 3/60 terminates because the reduced fraction is 1/20, and 20 = 2 * 2 * 5. A similar rule applies to non-integer numbers in computers. The fractional part is expressed as a binary fraction in the machine, so a decimal value is not exact unless the denominator of its fractional form is a power of 2. For example, .25 is exact inside a computer because .25 = 1/4, and 4 = 2 * 2. But .1 is approximate because .1 = 1/10, and 10 = 2 * 5. That was a problem in the Gulf War when a Patriot missile failed to intercept a Scud, with fatal results. The value in an internal counter (which incremented 10 times per second) was multiplied by .1 to obtain time. But the system had been running continuously for 4 days, so the error in .1 was magnified to about 1/3 second (I think). Some programming languages have a number format for financial computation where decimal values must be exact. However, this format doesn't have the great range of magnitude that you need for scientific and engineering work. -- Paul Hirose sofajpl.com

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