I have said it before and I will say it again: you need to set the default "digits" setting to a higher value. I don't think you can do in Wolfram Alpha, but you must be able to do it in Mathematica. Of course, Mathematica is the computational engine behind Wolfram Alpha, but that does not mean a non-paying Alpha user has access to all the capabilities of a paying Mathematica owner. Aloha does not want a remote user to re-set the basic Mathematica parameters in the host machine!
Exactly the same type of thing happens in Maple (and I previously showed you the output in another thread).