Why the nonsense number appears?

[Steve Horsley]

Ben O'Steen wrote:
> On Mon, October 31, 2005 10:23, Sybren Stuvel said:
>> Ben O'Steen enlightened us with:
>>> Using decimal as opposed to float sorts out this error as floats are
>>> not built to handle the size of number used here.
>> They can handle the size just fine. What they can't handle is 1/1000th
>> precision when using numbers in the order of 1e10.
>>
> 
> I used the word 'size' here incorrectly, I intended to mean 'length'
> rather than numerical value. Sorry for the confusion :)
> 

Sybren is right. The problem is not the length or the size, it's 
the fact that 0.039 cannot be represented exactly in binary, in 
just the same way that 1/3 cannot be represented exactly in 
decimal. They both give recurring numbers. If you truncate those 
recurring numbers to a finite number of digits, you lose 
precision. And this shows up when you convert the inaccurate 
number from binary into decimal representation where an exact 
representation IS possible.

Steve