Re: Precision of a number raised to a power

*To*: mathgroup at smc.vnet.net*Subject*: [mg73511] Re: Precision of a number raised to a power*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 21 Feb 2007 01:36:26 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <erelt5$7np$1@smc.vnet.net>

Sonya wrote: > Hallo > I am new to Mathematica and I am thankful to any help regarding the following. > If I have something like a^b . The a is any arbitrary decimal number (let us say of precision double) the b are numbers from 1-10 (exact numbers without a point). > What will be the precision of the above expression after raising a to the powers from 1-10. > > Many thanks in advance > Sonya > Hi Sonya, The precision of the results does not change: since you have a mix of hardware precision numbers and exact numbers the overall precision is lowered to machine precision and the computations are done using the functions implemented in the hardware. Detailed explanations are given in "The Mathematica Book Online / Advanced Mathematics in Mathematica / Numbers / 3.1.4 Numerical Precision", available at http://documents.wolfram.com/mathematica/book/section-3.1.4 To see the precision of a Mathematica expression, you can use the built-in function Precision [1]. For instance, In[1]:= a = 2.; In[2]:= Precision[a] Out[2]= MachinePrecision In[3]:= b = Range[10] Out[3]= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} In[4]:= Precision /@ b Out[4]= {Infinity, Infinity, Infinity, Infinity, Infinity, Infinity, Infinity, Infinity, Infinity, Infinity} In[5]:= a^b Out[5]= {2., 4., 8., 16., 32., 64., 128., 256., 512., 1024.} In[6]:= Precision /@ % Out[6]= {MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision, MachinePrecision} In[7]:= $MachinePrecision Out[7]= 15.9546 In[8]:= $Version Out[8]= 5.2 for Microsoft Windows (June 20, 2005) Regards, Jean-Marc [1] http://documents.wolfram.com/mathematica/functions/Precision