Yes, indeed, significant digits is certainly one of the terms I need. I couldn't for the life of me remember that term, nor the closely related 'margin of error' when I first wrote my original post...
Googling with "significant digits" hasn't yet led me to how to answer the question.
I did find this link to a pdf discussing estimation of required significant digits, and I think it very likely applicable to my question, but the paper is far enough above my head that I'm unable to use that link without further assistance.
Update: Ack, I hadn't seen trammell's post below when I posted this, I'm studying it now...
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