Re: Why Doesn't N[Pi,i] Give i Digits For Small i, Mathematica 4,on NT

• To: mathgroup at smc.vnet.net
• Subject: [mg20248] Re: [mg20220] Why Doesn't N[Pi,i] Give i Digits For Small i, Mathematica 4,on NT
• From: David Withoff <withoff at wolfram.com>
• Date: Fri, 8 Oct 1999 18:30:21 -0400
• Sender: owner-wri-mathgroup at wolfram.com

> If I execute:
>
> Table[{i, N[Pi, i]}, {i, 1, 20}]
>
> I get:
>
> {{1, 3.14159}, {2, 3.14159}, {3, 3.14159}, {4, 3.14159}, {5, 3.14159},
> {6,  3.14159}, {7, 3.14159}, {8, 3.14159}, {9, 3.14159}, {10, 3.14159},
> {11, 3.14159}, {12, 3.14159}, {13, 3.14159}, {14, 3.14159}, {15,
> 3.14159}, {16, 3.14159}, {17, 3.1415926535897932},
> {18, 3.14159265358979324}, {19, 3.141592653589793238},
> {20, 3.1415926535897932385}}
>
> I'd expect something like
> {{1,3},{2,3.1},{3,3.14},{4,3.141},{5,3.1416},{6,3.14159},{7,3.141593},....
>
> It seems N[] only works as expected above 16 digits of requested
> precision.
>
> Is my expectation wrong?  What should I do to get what I want?
>
> My platform is WinNT 4 SP4.

N[expr, i] for i less than machine precision does the calculation
using machine precision and returns a machine number as a result.
Machine numbers are displayed using the default precision (6 digits).

You can use SetPrecision to set a precision less than machine precision.

In[1]:= Table[{i, SetPrecision[Pi, i]}, {i, 1, 5}]

Out[1]= {{1, 3.}, {2, 3.1}, {3, 3.14}, {4, 3.142}, {5, 3.1416}}

If you just want to control the display, you can do that using
functions such as NumberForm.

In[2]:= Table[{i, NumberForm[N[Pi],i]}, {i, 1, 5}]

Out[2]= {{1, 3.}, {2, 3.1}, {3, 3.14}, {4, 3.142}, {5, 3.1416}}

You can change the default display precision in OutputForm using
Developer`SetSystemOptions["MachineRealPrintPrecision" -> i] or
in StandardForm or TraditionalForm using the PrintPrecision option
in the Option Inspector.

Dave Withoff
Wolfram Research

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