Depends on where you are publishing it. For example, APA (psych) journals specify p < .001 (without the lead zero which Sal Mangiafico uses for values that can't go above 1 ... I assume this is an example of the formatting differences between his discipline and mine), but in areas like discoveries in physics the 5 sigma rule is used, which would require more digits for small ps.
Thank you Sal Mangiafico Sir. I also totally agree with Daniel Wright Sir that this concept is both journal and discipline specific, from what I have learnt.