Significant digit measuring

[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 ([e-mail])

[Victor Bazarov]

mrstephengross wrote:

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

Actually, from what I remember, all numbers you have here have the same
number of significant digits: 3, the leading (and trailing) zeros do not
count as significant.

And then there is no such thing as "significant digits" in a double. What
may appear as 0.0103 to you (in the output), in fact is probably something
like 0.010299999999999998 in the computer. IOW, all digits (16 or so) are
significant in a 'double'.

V

[mrstephengross]

>What may appear as 0.0103 to you (in the output), in fact is probably
something
like 0.010299999999999998 in the computer. IOW, all digits (16 or so)
are
significant in a 'double'.

Darn! I suspected this was the case...

--Steve

[Mark P]

Victor Bazarov wrote:

mrstephengross wrote:

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

Actually, from what I remember, all numbers you have here have the same
number of significant digits: 3, the leading (and trailing) zeros do not
count as significant.

Mostly true, except that trailing zeros may be significant. Universally
(I believe) 0.103000 is regarded as having 6 significant digits. For
trailing zeros to the left of the decimal point it's ambiguous. 103000
may have from 3 to 6 significant digits. According to one convention,
one uses an overbar in such cases to mark the least significant digit.