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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Fri, 13 Feb 2015 14:49:13 -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 2:40 PM, Ian Kelly <ian.g.kelly@gmail.com> wrote:
> On Fri, Feb 13, 2015 at 2:22 PM, Grant Edwards <invalid@invalid.invalid> =
wrote:
>> On 2015-02-13, Dave Angel <davea@davea.name> wrote:
>>> On the other hand, the Decimal package has a way that the programmer
>>> can tell how many digits to use at each stage of the calculation.
>>
>> That's what surpised me.  From TFM:
>>
>> https://docs.python.org/2/library/decimal.html:
>>
>>  * The decimal module incorporates a notion of significant places so tha=
t
>>    1.30 + 1.20 is 2.50. The trailing zero is kept to indicate
>>    significance. This is the customary presentation for monetary
>>    applications. For multiplication, the =E2=80=9Cschoolbook=E2=80=9D ap=
proach uses
>>    all the figures in the multiplicands. For instance, 1.3 * 1.2 gives
>>    1.56 while 1.30 * 1.20 gives 1.5600.
>
> Huh. That approach for multiplication is definitely not what I was
> taught in school. I was taught that the number of significant digits
> in the product is the lesser of the number of significant digits in
> either of the measured multiplicands. So 1.30 * 1.20 would be 1.56,
> while 1.3 * 1.2 would just be 1.6. Wikipedia appears to agree with me:
>
> http://en.wikipedia.org/wiki/Significance_arithmetic#Multiplication_and_d=
ivision_using_significance_arithmetic
>
> Moreover:
>
>>>> D('1.304') * D('1.204')
> Decimal('1.570016')
>>>> D('1.295') * D('1.195')
> Decimal('1.547525')
>
> So 1.30 * 1.20 could be written approximately as 1.56 =C2=B1 0.01. Given
> that, I don't understand how the trailing zeros in 1.5600 could
> possibly be considered significant.

I guess the point here is that the paragraph isn't really talking
about significance arithmetic; it's explaining how it decides how many
digits to keep in the result. It may be fine for 1.30 * 1.20 to return
1.56, but it would be very confusing if 1.35 * 1.25 returned 1.69
instead of 1.6875. The wording of the paragraph seems misleading,
though.