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Check the screen shot. Why I'm getting 999s? It is suppose to be 127,977.52

enter image description here

Thanks in advance,


Quick solution: AccountingForm[58156.48 + 69821.04, 16]

And thanks to Yves Klett

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    $\begingroup$ Welcome! The bugs tag is for confirmed bugs only. $\endgroup$ – Yves Klett Nov 24 '14 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 Nov 24 '14 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 Nov 24 '14 at 17:24
  • $\begingroup$ Thanks checking those links, when I posted didn't saw those links. $\endgroup$ – Kruz Nov 24 '14 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 Nov 24 '14 at 17:27
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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.
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  • $\begingroup$ Thanks 58156.4820 + 69821.0420 // InputForm That is exactly what I was looking for. $\endgroup$ – Kruz Nov 24 '14 at 18:58

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