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Re: beauty or accuracy

• To: mathgroup at smc.vnet.net
• Subject: [mg103882] Re: beauty or accuracy
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sat, 10 Oct 2009 07:10:18 -0400 (EDT)

On 10/9/09 at 7:18 AM, zhengji.li at gmail.com (Li Zhengji) wrote:

>Hi all,
>
>42500 - 1907.25 = 40592.8
>(http://www.wolframalpha.com/input/?i=42500+-+1907.25)

>I do believe that it is because Mathematica "thinks" it's *better*
>to limit the result to six digits, so 0.75 is rounded to 0.8.

>But, don't you think that the result is a little strange, or
>inaccurate?

Not at all. By default Mathematica *displays* machine precision
numbers as being only 6 digits. But the actual value used by
Mathematica has more digits. That is

In[1]:= x = 42500 - 1907.25

Out[1]= 40592.8

In[2]:= RealDigits[x]

Out[2]= {{4,0,5,9,2,7,5,0,0,0,0,0,0,0,0,0},5}