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Re: Precision
Posted:
Jan 7, 2013 11:05 PM


Of course in the case of dollars and cents, one should not ordinarily need to worry about loss of precision  unless one is dealing with "exact" quantities on the order of the U.S. National Debt, which is roughly 2 * 10^13 and hence, including cents, would use 16 digits.
On Jan 7, 2013, at 12:38 AM, Andrzej Kozlowski <akozlowski@gmail.com> wrote:
> > On 5 Jan 2013, at 08:19, Rob Ryan <tio540s1@gmail.com> wrote: > >> My frustration is growing. I simply want to add (for example): >> 103971.66+52282.64+2998.27. These are dollars and cents and I'd like to keep the cents. But when I input that line, I get 159923. When I input: N[(103971.66+52282.64+2998.27),20] I STILL get 159923. What do I do to get 159952.57? I've used "SetPrecision", etc. with still no result. >> I note that when I type 103971.66 and hit shiftreturn, the output is 103972. If I then type "InputForm[%]" I get 103971.66. >> >> There simply has to be an easy way to add these numbers  any calculator watch can do it! > > > In this case you can simply use NumberForm: > > NumberForm[103971.66 + 52282.64 + 2998.27, 8] > > 159252.57 > > However, this approach will not always work (to understand why you have to first understand that Mathematica's approximate reals are not what you probably think they are) > > A much more reliable way is to do such computations using exact numbers. This will never give you a wrong answer: > > QuotientRemainder[10397166 + 5228264 + 299827, 100] > > {159252, 57} > > If you don't like this, you would be better off using a calculator watch.
 Murray Eisenberg murray@math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 5491020 (H) University of Massachusetts 413 5452838 (W) 710 North Pleasant Street fax 413 5451801 Amherst, MA 010039305



