When to use Noble gas core in writing electron configurations?

You can write out the full electron configuration any time you feel like taking the time.  The noble gas core configuration just exists as a shortcut for larger atoms.  It's convenient because it shows only the outer-most electrons, which are usually the only electrons we care about in chemistry anyway.  I typically use noble gas core configurations for any atom on the third row or below, but there's no hard and fast rule about which is appropriate in each situation.  It's kind of like using scientific notation.  Should you write 628 000 000 000, or should you write 6.28x10^11?  It just depends on what you're trying to show.

I hope that helps.  Good luck!