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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Fri, 13 Feb 2015 14:01:11 -0700
Subject: Re: Floating point "g" format not stripping trailing zeros
To: Python <python-list@python.org>
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On Fri, Feb 13, 2015 at 1:33 PM, Grant Edwards <invalid@invalid.invalid> wr=
ote:
> On 2015-02-13, Ian Kelly <ian.g.kelly@gmail.com> wrote:
>> On Fri, Feb 13, 2015 at 7:02 AM, Grant Edwards <invalid@invalid.invalid>=
 wrote:
>>> On 2015-02-12, Ian Kelly <ian.g.kelly@gmail.com> wrote:
>>>> On Thu, Feb 12, 2015 at 1:23 PM, Hrvoje Nik=C5=A1i=C4=87 <hniksic@gmai=
l.com> wrote:
>>>>
>>>>> {:.15g} is supposed to give 15 digits of precision, but with trailing
>>>>> zeros removed.
>>>>
>>>> The doc says with "insignificant" trailing zeros removed, not all
>>>> trailing zeros.
>>>
>>> Can somebody explain the difference between "significant" and
>>> "insignificant" tailing zeros to somebody who barely passed his single
>>> numerical methods class?  [Though I have, on occasion, had to tinker
>>> with the innards of SW floating point libraries and could fish a
>>> hardcopy of IEEE-754 out of a filing cabinet if needed.]
>>
>> Significant digits are within the precision of the calculation.
>> Writing 1.230 indicates that the fourth digit is known to be zero.
>> Writing 1.23 outside a context of exact calculation indicates that the
>> fourth digit is unknown due to insufficient precision.
>
> I knew that, but I was asking in the context of float/decimal's
> formatting function.  I didn't realize that float and/or decimal had a
> "significant digit" property, and therefore possess significant vs.
> insignificant trailing zeros when represented in base-10.

A Decimal object consists of a sign, a tuple of decimal digits, and an
exponent. If the digits are, e.g, (1, 2, 3, 0, 0, 0), then that would
be equal to the Decimal with the digits (1, 2, 3) and the same sign
and exponent, but the explicit presence of the trailing zeros
indicates their significance. If this doesn't answer your question,
then I'm not really sure what you're asking.