How to detect a double's significant digits

[AnswerGuy]

James Stroud wrote:
> Significant digits are an accounting concept. As such, it is up to
the
> accountant to keep track of these as only she knows the precision of
her
> measurements.
>
> Koan for the day:

> What are the significant digits of 0.1?

> Hint:

> >>> `0.1`

> James

> On Thursday 05 May 2005 10:37 am, so sayeth 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

 Since "significant digits" is a representation concept rather
 than a mathematical one I'd be inclined to convert the value
 to a string, split on the decimal point and return the length
 of that.

 A naive approach:

    def sigdigits(x):
       return len( ("%s" % float(x)).split('.')[1])


 ... but this gives bogus results for integers (saying that they
 have "one" significant digit when, by your definition they have
 zero.

 I suppose you have to amend your definition to handle numbers
 larger than 1 and I have to do something different than just
 coercing into a float().

    def sigdigits(x):
       assert float(x) == x  # raise an exception if we can't float it
       ret = 0
       strep = float(x)
       (whole, fraction) = strep.split('.')
       if int(fraction) > 0:
           ret += len(fraction)
       if int(whole) > 0:
           ret += len(whole)

 ... I think that should do it.  We could explicitly trim leading zeros
 from the whole number part and trailing zeros from the fractional
part.
 However I think the string representation (in Python's built-ins)
 guarantees us that there will be no leading or trailing zeros unless
 the part we're looking at is numerically equivalent to zero.

JimD