The question http://mathoverflow.net/questions/78576/am-i-allowed-to-do-non-rigorous-numerical-analysis has one close vote at the moment. I think it is interesting, although obviously subjective, and I'd be glad to hear from some experienced editors how they would treat this.

Basically, the question is the following. There is a real number a which plays an important role in the OP's paper. There is no closed formula for a, but he can approximate it numerically. If he publishes 5 digits of a, is that an implicit claim that he has rigorously proven a to lie in an interval of width 10^{-5}, or is it enough to have used numerical algorithms which are generally reliable?

My two-bits as a numerical analyst: it's entirely acceptable to state the computed 'a' is a numerical approximation to the desired 'a'. It's not OK in general to claim that the computed a is correct to 5 digits. In specific instances, one may assert: since the original problem has some features X, and we know numerical algorithms Y converge to the solution of the problem given X, the computed a is indeed a good approximation.

Without knowing more about the setting it's hard to provide more concrete advice. However, consider the following scenario: a is a global minimizer of a function with many local minima. There may be a numerical strategy which is based on computing the residual, and the computed a may indeed reduce the residual to 10^-5. That doesn't imply a is close to the computed a.

I'm sorry to be nit-picky.