We are a decimal numbering system people. We are always getting into trouble with representing decimal numbers in binary. It is almost hopeless to try to explain to a non-mathematician or non-computer programmer why 0.1 cannot be represented exactly in a computer. They just know you are an idiot. The problem is more than just thinking that calculations to 16 places are accurate when we are dealing with things where we may not even know if the first significant digit is accurate. Take oil reserves for example. Legal rules are picky. If you want to replace a method of calculating something legally defined with a better method, it is not acceptable if it does not give the exact same answer as the old method, even if the new method is more accurate.
There is a new IEEE decimal float standard kicking around. It could address many problems we run into when trying to do calculations which are critical in decimal using binary floats. Money is a big one. I always do money calculations in pennies for that reason. But I believe conversions in monetary exchanges are given in decimal fractions, not binary fractions. I might be wrong. But we either use floating point to do the calculations or go to a lot of trouble to do them in decimal. But when making such conversions legally they must be exact as described in the conversion method. Can't be off even a penny. Feet or meters? We like round numbers. In the USA we convert feet to meters and end out with several decimal places. Makes metric look difficult. We seldom realize that converting from meters to feet we end out with just as nasty looking numbers. I saw where in a baseball field they had put the distance in feet, say 350 feet to the fence, then put under it the equivalent in meters to 2 decimal places. I doubt that the distance in feet was anywhere near that accurate. Why didn't they just put 107 meters for the distance? Probably just as accurate. But it made metric look bad. We just love doing calculations to ridiculous amounts because it is fun knowing how hard it would be to do it on pencil and paper. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
