Check the screen shot. Why I'm getting 999s? It is suppose to be 127,977.52
Thanks in advance,
Quick solution: AccountingForm[58156.48 + 69821.04, 16]
And thanks to Yves Klett
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- 1$\begingroup$ Welcome! The bugs tag is for confirmed bugs only. $\endgroup$Yves Klett– Yves Klett2014-11-24 17:16:34 +00:00Commented Nov 24, 2014 at 17:16
- $\begingroup$ Not to worry. What you are seeing is not a bug but a result of machine precision arithmetic. This is actually a duplicate of mathematica.stackexchange.com/q/5580/131. Also useful: floating-point-gui.de/basic $\endgroup$Yves Klett– Yves Klett2014-11-24 17:20:06 +00:00Commented Nov 24, 2014 at 17:20
- $\begingroup$ There are only two digits after decimal in the input, so ideally it output only 2 digits for additions or subtractions. Is there a way to get output like 127,977.52 in the above case? $\endgroup$Kruz– Kruz2014-11-24 17:24:52 +00:00Commented Nov 24, 2014 at 17:24
- $\begingroup$ Thanks checking those links, when I posted didn't saw those links. $\endgroup$Kruz– Kruz2014-11-24 17:25:38 +00:00Commented Nov 24, 2014 at 17:25
- $\begingroup$ The only way to "fix" this would be to use exact numbers. Most of the time this will not be neccessary however. $\endgroup$Yves Klett– Yves Klett2014-11-24 17:27:17 +00:00Commented Nov 24, 2014 at 17:27
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1 Answer
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1 This is a problem for anything that uses machine precision floats, e.g. Mathematica, Matlab, C, etc.
Consider the simpler example $1/10$. In base 10, this fraction has the finite decimal expansion $$ 1/10 = 0.1 $$ But your machine would store this number (and all floats) in binary. The problem is, in binary $1/10$ has the infinite decimal expansion $$ 1/10 = \left(0.000\overline{1100}\right)_2 $$ This means your machine must to round (since it can't store infinite digits). This introduces error.
Now for your problem, we can see your decimals don't have a finite expansion in binary using RealDigits:
RealDigits[58156.48, 2] {{1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1}, 16}
RealDigits[69821.04, 2] {{1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1}, 17}
As Yves said in the comments, a fix in Mathematica is to avoid machine precision and use exact precision. Here I am forcing both numbers to have the first 20 digits correct:
58156.48`20 + 69821.04`20 // InputForm 127977.52`20.
- $\begingroup$ Thanks 58156.48
20 + 69821.0420 // InputForm That is exactly what I was looking for. $\endgroup$Kruz– Kruz2014-11-24 18:58:30 +00:00Commented Nov 24, 2014 at 18:58