[Python-ideas] Python Numbers as Human Concept Decimal System

[Steven D'Aprano]

On Wed, Mar 05, 2014 at 12:10:18AM -0800, Andrew Barnert wrote:

> Anyone with a middle school expectation will expect 1/3 to be a 
> fraction—or, at least, something they can multiply by 3 to get exactly 
> 1. 

Not a very good example -- that happens to work for Python floats (which 
are C doubles under the hood):

py> (1/3)*3 == 1
True
py> (1/3 + 1/3 + 1/3) == 1
True


But it *does not work* with Decimal, at least not with the default 
precision:

py> from decimal import Decimal
py> (Decimal(1)/3)*3
Decimal('0.9999999999999999999999999999')


Decimal is not a panacea! It does not eliminate floating point issues. 
Between 1 and 100, there are 32 Decimal numbers that fail the test that 
(1/n)*n == 1, and only two floats. 

Between 1 and 100, there are only four floats where 1/(1/n) does not 
equal n: 49 93 98 and 99. In comparison, there are 46 such failing 
Decimals, including 6 7 and 9.



-- 
Steven