How to detect a double's significant digits

[mrstephengross]

Hi all... How can I find out the number of significant digits (to the
right of the decimal place, that is) in a double? At least, I *think*
that's what I'm asking for. For instance:

0.103 --> 3
0.0103 --> 4
0.00103 --> 5
0.000103 --> 6
0.0000103 --> 7

Thanks in advance!
--Steve (mrstephengross at hotmail.com)