Original Translation
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In base 2, 1/2 = 0.1, 1/4 = 0.01, 1/8 = 0.001, etc. .2 equals 2/10 equals 1/5, resulting in the binary fractional number 0.001100110011001...
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Floating point numbers only have 32 or 64 bits of precision, so the digits are cut off at some point, and the resulting number is 0.199999999999999996 in decimal, not 0.2.
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A floating point number's ``repr()`` function prints as many digits are necessary to make ``eval(repr(f)) == f`` true for any float f. The ``str()`` function prints fewer digits and this often results in the more sensible number that was probably intended::
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>>> 1.1 - 0.9 0.20000000000000007 >>> print(1.1 - 0.9) 0.2
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One of the consequences of this is that it is error-prone to compare the result of some computation to a float with ``==``. Tiny inaccuracies may mean that ``==`` fails. Instead, you have to check that the difference between the two numbers is less than a certain threshold::
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epsilon = 0.0000000000001 # Tiny allowed error expected_result = 0.4 if expected_result-epsilon <= computation() <= expected_result+epsilon: ...
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Please see the chapter on :ref:`floating point arithmetic <tut-fp-issues>` in the Python tutorial for more information.
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Why are Python strings immutable?
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There are several advantages.
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One is performance: knowing that a string is immutable means we can allocate space for it at creation time, and the storage requirements are fixed and unchanging. This is also one of the reasons for the distinction between tuples and lists.