Re: FractionalPart

• To: mathgroup at smc.vnet.net
• Subject: [mg31242] Re: [mg31232] FractionalPart
• From: BobHanlon at aol.com
• Date: Tue, 23 Oct 2001 04:53:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/10/20 5:21:59 AM, erfa11 at hotmail.com writes:

>I am new in Mathematica(also in english), and I have this question:
>I would like to know the behavior of the function FractionalPart.
>See here:
>
>In[1]:= a=Range[9]^2
>Out[1]= {1,4,9,16,25,36,49,64,81}
>
>In[2]:= x=Exp[.5 Log[a]]
>Out[2]= {1,2.,3.,4.,5.,6.,7.,8.,9.}
>
>In[3]:= FractionalPart[x]
>Out[3]= {0,0.,4.444089x10^-16,0.,0.,1.,0.,0.,1.,1.77639x10^-15}
>
>But it shoud be 0., all of them,no?
>

You are seeing the results of using machine precision.

a = Range[9]^2

{1, 4, 9, 16, 25, 36, 49, 64, 81}

Your results are not integers.  The display precision merely makes them
appear to be.

(x =Exp[0.5*Log[a]])//InputForm

{1, 2., 3.0000000000000004, 4.,
4.999999999999999, 6.,
6.999999999999999,
7.999999999999998,
9.000000000000002}

FractionalPart[x]//InputForm

{0, 0., 4.440892098500626*^-16, 0.,
0.9999999999999991, 0.,
0.9999999999999991,
0.9999999999999982,
1.7763568394002505*^-15}

For exact results, use exact numbers

x =Exp[Log[a]/2]

{1, 2, 3, 4, 5, 6, 7, 8, 9}

FractionalPart[x]

{0, 0, 0, 0, 0, 0, 0, 0, 0}

```

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