Finding the number of places after the decimal point of a Double

var precision = 0;
var x = 1.345678901m;

while (x*(decimal)Math.Pow(10,precision) != 
         Math.Round(x*(decimal)Math.Pow(10,precision))) 
   precision++;

precision will be equal to the number of significant digits of the decimal value (setting x to 1.23456000 will result in a precision of 5 even though 8 digits were originally specified in the literal). This executes in time proportional to the number of decimal places. It counts the number of fractional digits ONLY; you can count the number of places to the left of the decimal point by taking the integer part of Math.Log10(x). It works best with decimals as they have better value precision so there is less rounding error.

There's no easy way, especially since the number of digits mathematically speaking might be far more than displayed. For example, 4.5565 is actually stored as 4.556499999999999772626324556767940521240234375 (thanks to harold for calculating that). You're very unlikely to find a useful solution to this problem.

EDIT

You could come up with some algorithm that works like this: if, as you calculate the decimal representation, you find a certain number of 9s (or zeros) in succession, you round up (or down) to the last place before the series of 9s (or zeros) began. I suspect that you would find more trouble down that road than you would anticipate.