Floating point "g" format not stripping trailing zeros

[Ian Kelly]

On Fri, Feb 13, 2015 at 7:02 AM, Grant Edwards <invalid at invalid.invalid> wrote:
> On 2015-02-12, Ian Kelly <ian.g.kelly at gmail.com> wrote:
>> On Thu, Feb 12, 2015 at 1:23 PM, Hrvoje Nikšić <hniksic at gmail.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.