I had a very simple program written in Python 2.6: As follows z=[1.2,2.3,3.6] and asked to print z, the out was [1.2, 2.2999999999996,3.599999999996]. I am wondering what is the property of 1.2, i changed the position, from the first to the middle to the last etc. but the output is only 1.2, I don't know if 1.2 has any property.
Not sure if this answers your question, but those numbers are not exactly representable in binary. Each is converted decimal to binary on input, and then binary to decimal for printing.
That said, I would have expected a few more 9s in the latter two, since presumably the values are kept as machine doubles and those are almost always 16 or so digits (53 bits mantissa).
All numbers are represented in binary in computers. This has consequences regarding floating point numbers as Daniel mentioned. (Most floating point numbers cannot be exactly represented in binary, while some can be.)
Maybe you will find this helpful:
http://docs.python.org/2.6/tutorial/floatingpoint.html
More in depth:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.6768
That Python document is interesting (and the Goldberg reference is definitive). One thing about the first one though. There is the claim: "On most machines, if Python were to print the true decimal value of the binary approximation stored for 0.1, it would have to display
0.1000000000000000055511151231257827021181583404541015625
instead!" I suspect the author confused machine double floating point mantissa bit lengh with digit length.
@Daniel I have not confused. If python shows double floating point, then it should should for all, am i correct? Instead it shows for all other than 1.2 that is the problem.
@Prasanth G. Narasimha-Shenoi Apologies for my lack of clarity. By "the author" I meant the one who wrote that particular piece of Python documentation, at
http://docs.python.org/2.6/tutorial/floatingpoint.html
Your note was not at issue in my remark.
As for what Python, or other languages, show of floating point numbers that arise for decimals that are not exactly representable in binary, it tends to vary depending on how many digits get shown, and how hard the interpreting code tries to coerce to a "short" decimal, say within an ULP of the binary value.
There is also an influence from how the number was formed. For example, 3*1.2 might not come out quite the same as 3.6 because roundoff error in the computation could move it slightly from the binary representation of 3.6. This sort of thing can be particularly bedeviling in loops that multiply or increment a decimal value, e.g. for (i=1.2; i
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