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Re: Base 10 to Base 2 conversion error ?
So, it's solved by the first case tried -> 0.01 doesn't work. Sounds like the enumeration search worked quite well to answer the stated question. It's certainly true that one can use lots and lots of digits, but it's expensive, and what's the point? In financial markets, interest rates are stated in "basis points", which are hundredths of a percent, so in practice the precision of computation cannot exceed one part in ten thousand. The classic non-religious reason for a bank to do things to the exact penny, and to use a carefully-chosen roundoff method for fitting the results of an interest calculation into the result field, is to help the detection of a classic fraud, where the less-than-a-penny roundoffs are deposited in an account which is periodically emptied by a conspiritor. (The other method of detection is to look for unbalanced accounts, where outgo does not equal income plus interest on balance.) The other reason is that retail customers complain if things aren't done to the penny. But is anyone using Mathematica to prepare retail bank statements? I think not. So, the question remains: why isn't one part in a billion sufficient precision? Joe Gwinn