[Tutor] How to correct decimal addition.

[spir]

On 01/26/2014 04:22 AM, Keith Winston wrote:
> On Sat, Jan 25, 2014 at 5:09 PM, Oscar Benjamin
> <oscar.j.benjamin at gmail.com> wrote:
>> Perhaps it would be better though to point at this:
>>>>> round(D('0.123456'), 3)
>> Decimal('0.123')
>
> I think you are right. I didn't even think of round(). I think we have
> confounded two issues in this thread, the internal
> representation/accuracy, and the final presentation. They aren't
> really the same thing, unless we force them to be (i.e. using ints).

Yes. Side-note below.

In programming, there is a general confusion between ideas, such as <the number 
-1.23> and their representations, like "-1.23" "minus one dot twenty three", 
"moins un virgule vingt-trois", "-1,23", or varipus possible strings of bits. 
There are outer written or spoken representations (numerals, for numbers) and 
internal representations in memory, which we could call "raw data". Raw data are 
meaningless (and type-less). Obviously, many truely believe there are data with 
meaning or type, that is ideas, *in* a machine; especially many speak and 
obviously think as if there were _numbers_ in a computer; as if a machine had a 
mind and thought... Numbers and other ideas are only in "heads" of psychical 
(mental) living things, as far as we know. there are no numbers, colors, texts, 
characters, weapons... in a machine ;-)

The internal representation is no less a representation and a pure convention. 3 
can be written
	vvvvvv^^
(with, say, bits 'on' and 'off')
it is a pure conventional representation (albeit simple & logical), and works 
because routines supposed to operate on numbers take this conventional 
representation for granted, both for operations and for input/output conversions 
to/from outer written representations.

In both internal and external representations there may be issues related to the 
base (eg in python we can also write hex or bin numbers). And a major issue, 
that will last as long as CPU's don't process decimal fractionals natively 
(so-to-say), is the clash between our expectations related to outer decimals and 
the inner processing in binary representation.

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