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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Fri, 13 Feb 2015 14:40:01 -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 2:22 PM, Grant Edwards <invalid@invalid.invalid> wr=
ote:
> 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 that
>    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 app=
roach 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_div=
ision_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.