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Re: Precision of output


On 5/17/04 at 3:22 AM, spam at husumtoften.invalid (Per R¯nne) wrote:

>If I write:
>
>N[4209/0.14,100] I get: 30064.3

>But if I write N[420900/14,100] I get:
>30064.
>285714285714285714285714285714285714285714285714285714285714285714
>285714\ 28571428571428571428571

>Why the difference? I thought N determined the number of digitals
>shown - but I seem to have some problems with this function. And it
>is not in this example only.

The difference is caused by using an exact number in one case and an inexact number in the other case. In particular the documentation states:

Unless numbers in expr are exact, or of sufficiently high precision, N[expr, n] may not be able to give results with n digit precision. 

When you write 0.14 you are expressing a number with much less precision than 100 digits. Consequently, there is no valid way to get 100 digit precision from 4209/.014
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