I'm working on a scientific paper in which goodness-of-fit and a parameter are estimated by a $\chi^2$ minimization, and I'd like to know whether there is a general rule for how many significant figures one should quote for the value of the $\chi^2$ and its resulting P-value.
In particular I'm fitting one parameter from data in 31 bins, each with its contents in the gaussian regime. I'd guess the precision of my minimization algorithm is not the limiting factor (my code spits out $\chi^2$ = 38.8898 / 30, so the P-value is something like 0.1282) for signifcant figures, but what is? Is it the number of degrees of freedom? The degree to which the gaussian assumption is invalid in the least-populated bin(s)? Most papers I see typically quote to tenths in $\chi^2$ (so 38.9 / 30 in my case) and hundredths in P-value (0.13 for me), but I'm not sure if that's always reasonable.
P.S.- I'd like to apologize if any terminology I used is funny: in physics we use annoyingly non-standard terms when discussing statistics.