Precision and rounding issue?

Questions
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1

Hello,
I have been interfacing to another program using the .NET interface, and found that real values which at their source have at least 7 digits of precision are being rounded. That lead me to read them as strings and apply ToExpression, with the same result.Since ToExpression uses input rules, i tried just a direct keyboard input, with the same results. Have I forgotten something? Can anyone tell me why I am failing to get a real number of 7 digits into Mathematica? I’m on the current release of 10 on win 7.

In[1]:= real = 39.99998

Out[1]= 40.

In[2]:= N[real, 15]

Out[2]= 40.

In[3]:= 100000 real

Out[3]= 4.*10^6

In[4]:= Precision[real]

Out[4]= MachinePrecision

In[5]:= $MachinePrecision

Out[5]= 15.9546
2

It is just a matter of output formating, which is abbreviated by default. Try

FullForm[real]
NumberForm[real, 10]
RealDigits[100000 real]

The function N is meant to turn exact symbolic numbers into floating-point numbers. It does not do much to numbers that are already floating-point. The whole matter is confusing, though. Mathematica has formating conventions that are fine most of the times, but can run against expectations in some cases.

3

Yes, Thank you. The problem was just formatting, which is likely in the definition of StandardForm. Does anyone know how to customize in a notebook the number of digits MAthematica is willing to display in StandardForm?

4

I believe this might provide what you want:

SetOptions[EvaluationNotebook[], PrintPrecision -> 10]

with the caveat from the documentation for ‘PrintPrecision’:

“This function has not been fully integrated into the long-term Wolfram Language, and is subject to change.”

5

To globally set the number of digits displayed, use Edit → Preferences:

Preferences.png
Preferences.png548×530 52.5 KB

For an individual notebook, PrintPrecision can be changed through Option Inspector

6

Thank you all. This was just what I needed!