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Precision is Everything

Want to visit the moon for $5? It’s easy, just send the money and I can get you there. Actually, you’re there now, ±106 km! That’s not really what you expected, was it? Precision is everything in engineering and science, but traditional computer math libraries like cmath.h do not track the precision of quantities you enter, and they certainly won’t propagate them through your equations!

In Math Touch, every number keeps track of its precision, whether it’s the default significant figure tracking, or the more advanced parenthetical or ± notation. Arithmetic operations use first-order precision propagation and trigonometric functions use second order propagation. And just for completeness, unit conversions and equation constants can be set as “Pure” so their lack of uncertainty doesn’t result in a couple of billion extra digits.
From the Earth to the Moon: 384000 km

Earth & MoonImage Credit: JPL, NASA
373.15 K

I sat in on a rehearsal for a design review for AggieSat-1 shortly after arriving at Texas A&M.  A student had listed the maximum allowed temperature of one component as 373.15 K.  The professor noticed immediately and asked where this 5-significant figure temperature requirement had come from.  The student followed back through the documentation to discover the original requirement was actually 100. ºC, but when asked to convert all temperatures into Kelvin for the presentation, the student had simply added 273.15.  MS Excel dutifully reported all the non-zero digits, and the result was a value with a precision much higher than we could measure or enforce.  Math Touch does not make these kinds of mistakes because it always tracks the precision of your values.