Hi Marco, thanks again for your reply much appreciated, I had resorted to using Round in the end and Ceiling also worked, what didn't work consistently was IntegerPart out of the 4 values, 3 would be ok and one of them not and then sometimes all 4 would be ok, that I found to be very disconcerting that it wasn't consistent. Anyway I have now utilized the Rationalize function and all is working perfectly now, thank you.

Paul.

Thank you very much for your quick replies, I do indeed see why I am getting the unexpected results, which now leaves me to ask this question. The line

u = N[Log[k]/Log[3], 10]

giving {6.000000000, 5.000000000, 3.000000000, 0} is clearly indicating that the numbers are 3 to some exact power, as in 3^6, 3^5, 3^3 and 3^0, so how would I extract the integer part not knowing it is an integer as this would be a test of many values?

Paul.

Hi Paul,

I suppose that this is a numerical effect. The elements of u are not exact numbers. It is easy to see as:

u = N[Log[k]/Log[3], 10] - {6, 5, 3, 0}

gives

{0.*10^-10, 0.*10^-10, 0.*10^-10, 0}

So the first entries are not exactly zero. This leads to the symptom that the small deviation is treated by Mathematica as if it was a small negative number. So that the displayed 6.00000000 you see is actually like a 5.999999999999999999999999.... that means that a tiny little number is subtracted from 6 so that the fractional part is nearly (and up to the precision you use) one.

You see that when you calculate:

FractionalPart[0. - N[Log[k]/Log[3], 10]]

(*{0., 0., 0., 0.}*)

and then (without the "." for the 0)

FractionalPart[0 - N[Log[k]/Log[3], 10]]

{-1.000000000, -1.000000000, -1.000000000, 0}

Another way of looking at your problem is to directly use the Logarithm to the right basis:

FractionalPart[N[Log[3, k], 10]]

which gives numerical zeros:

{0.*10^-10, 0.*10^-10, 0.*10^-10, 0}

I don't think that I explained this very well, but I hope you understand what I wanted to say.

Cheers,

M.