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#
SOME DESCRIPTIVE TITLE.
#
Copyright (C) 2001 Python Software Foundation
#
This file is distributed under the same license as the Python package.
#
FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
#
#
Translators:
#
python-doc bot, 2025
#
Takanori Suzuki <takanori@takanory.net>, 2025
#
#,
fuzzy
msgid ""
msgstr ""
"
Project-Id-Version
:
Python 3.15\n
"
"
Report-Msgid-Bugs-To
:
\n
"
"
POT-Creation-Date
:
2026-10-01 19:07+0000\n
"
"
PO-Revision-Date
:
2025-09-16 00:02+0000\n
"
"
Last-Translator
:
Takanori Suzuki <takanori@takanory.net>, 2025\n
"
"
Language-Team
:
Japanese (https://app.transifex.com/python-doc/teams/5390/
"
"
ja/)\n
"
"
Language
:
ja\n
"
"
MIME-Version
:
1.0\n
"
"
Content-Type
:
text/plain; charset=UTF-8\n
"
"
Content-Transfer-Encoding
:
8bit\n
"
"
Plural-Forms
:
nplurals=1; plural=0;\n
"
#:
../../tutorial/floatingpoint.rst:10
msgid
"Floating-Point Arithmetic: Issues and Limitations"
msgstr
""
#:
../../tutorial/floatingpoint.rst:12
msgid
""
"Floating-point numbers are represented in computer hardware as base 2 "
"(binary) fractions. For example, the **decimal** fraction ``0.625`` has "
"value 6/10 + 2/100 + 5/1000, and in the same way the **binary** fraction "
"``0.101`` has value 1/2 + 0/4 + 1/8. These two fractions have identical "
"values, the only real difference being that the first is written in base 10 "
"fractional notation, and the second in base 2."
msgstr
""
" 2 \n"
" **10 ** ``0.625`` 6/10 + 2/100 + 5/1000 "
" **2 ** ``0.101`` 1/2 + 0/4 + 1/8 \n"
" 10 2 "
""
#:
../../tutorial/floatingpoint.rst:19
msgid
""
"Unfortunately, most decimal fractions cannot be represented exactly as "
"binary fractions. A consequence is that, in general, the decimal floating-"
"point numbers you enter are only approximated by the binary floating-point "
"numbers actually stored in the machine."
msgstr
""
" 10 2 "
" 10 2 "
""
#:
../../tutorial/floatingpoint.rst:24
msgid
""
"The problem is easier to understand at first in base 10. Consider the "
"fraction 1/3. You can approximate that as a base 10 fraction::"
msgstr
""
" 10 1/3 "
" 10 ::"
#:
../../tutorial/floatingpoint.rst:27
msgid
"0.3"
msgstr
"0.3"
#:
../../tutorial/floatingpoint.rst:29
../../tutorial/floatingpoint.rst:33
msgid
"or, better, ::"
msgstr
" ::"
#:
../../tutorial/floatingpoint.rst:31
msgid
"0.33"
msgstr
"0.33"
#:
../../tutorial/floatingpoint.rst:35
msgid
"0.333"
msgstr
"0.333"
#:
../../tutorial/floatingpoint.rst:37
msgid
""
"and so on. No matter how many digits you're willing to write down, the "
"result will never be exactly 1/3, but will be an increasingly better "
"approximation of 1/3."
msgstr
""
" 1/3 "
" 1/3 "
#:
../../tutorial/floatingpoint.rst:41
msgid
""
"In the same way, no matter how many base 2 digits you're willing to use, the "
"decimal value 0.1 cannot be represented exactly as a base 2 fraction. In "
"base 2, 1/10 is the infinitely repeating fraction ::"
msgstr
""
"2 10 0.1 2 "
"2 1/10 ::"
#:
../../tutorial/floatingpoint.rst:45
msgid
"0.0001100110011001100110011001100110011001100110011..."
msgstr
"0.0001100110011001100110011001100110011001100110011..."
#:
../../tutorial/floatingpoint.rst:47
msgid
""
"Stop at any finite number of bits, and you get an approximation. On most "
"machines today, floats are approximated using a binary fraction with the "
"numerator using the first 53 bits starting with the most significant bit and "
"with the denominator as a power of two. In the case of 1/10, the binary "
"fraction is ``3602879701896397 / 2 ** 55`` which is close to but not exactly "
"equal to the true value of 1/10."
msgstr
""
""
" 53 "
"2 1/10 "
"``3602879701896397 / 2 ** 55`` 1/10 "
""
#:
../../tutorial/floatingpoint.rst:54
msgid
""
"Many users are not aware of the approximation because of the way values are "
"displayed. Python only prints a decimal approximation to the true decimal "
"value of the binary approximation stored by the machine. 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::"
msgstr
""
"Python "
" 2 10 "
" 10 "
"0.1 2 Python 10 "
"::"
#:
../../tutorial/floatingpoint.rst:60
msgid
""
">>> 0.1\n"
"0.1000000000000000055511151231257827021181583404541015625"
msgstr
""
">>> 0.1\n"
"0.1000000000000000055511151231257827021181583404541015625"
#:
../../tutorial/floatingpoint.rst:63
msgid
""
"That is more digits than most people find useful, so Python keeps the number "
"of digits manageable by displaying a rounded value instead:"
msgstr
""
"Python "
":"
#:
../../tutorial/floatingpoint.rst:66
msgid
""
">>> 1 / 10\n"
"0.1"
msgstr
""
">>> 1 / 10\n"
"0.1"
#:
../../tutorial/floatingpoint.rst:71
msgid
""
"Just remember, even though the printed result looks like the exact value of "
"1/10, the actual stored value is the nearest representable binary fraction."
msgstr
""
" 1/10 "
" 2 1/10 "
""
#:
../../tutorial/floatingpoint.rst:74
msgid
""
"Interestingly, there are many different decimal numbers that share the same "
"nearest approximate binary fraction. For example, the numbers ``0.1`` and "
"``0.10000000000000001`` and "
"``0.1000000000000000055511151231257827021181583404541015625`` are all "
"approximated by ``3602879701896397 / 2 ** 55``. Since all of these decimal "
"values share the same approximation, any one of them could be displayed "
"while still preserving the invariant ``eval(repr(x)) == x``."
msgstr
""
" 10 2 "
"``0.1`` ``0.10000000000000001`` "
"``0.1000000000000000055511151231257827021181583404541015625`` "
"``3602879701896397 / 2 ** 55`` 10 "
" ``eval(repr(x)) == x`` "
""
#:
../../tutorial/floatingpoint.rst:82
msgid
""
"Historically, the Python prompt and built-in :func:`repr` function would "
"choose the one with 17 significant digits, ``0.10000000000000001``. "
"Starting with Python 3.1, Python (on most systems) is now able to choose the "
"shortest of these and simply display ``0.1``."
msgstr
""
"Python :func:`repr` 17 "
"``0.10000000000000001`` Python 3.1 "
" ``0.1`` "
""
#:
../../tutorial/floatingpoint.rst:87
msgid
""
"Note that this is in the very nature of binary floating point: this is not a "
"bug in Python, and it is not a bug in your code either. You'll see the same "
"kind of thing in all languages that support your hardware's floating-point "
"arithmetic (although some languages may not *display* the difference by "
"default, or in all output modes)."
msgstr
""
"2 Python "
""
" "
"( "
"**** )"
#:
../../tutorial/floatingpoint.rst:93
msgid
""
"For more pleasant output, you may wish to use string formatting to produce a "
"limited number of significant digits:"
msgstr
""
"10"
":"
#:
../../tutorial/floatingpoint.rst:96
msgid
""
">>> format(math.pi, '.12g') # give 12 significant digits\n"
"'3.14159265359'\n"
"\n"
">>> format(math.pi, '.2f') # give 2 digits after the point\n"
"'3.14'\n"
"\n"
">>> repr(math.pi)\n"
"'3.141592653589793'"
msgstr
""
">>> format(math.pi, '.12g') # 12 \n"
"'3.14159265359'\n"
"\n"
">>> format(math.pi, '.2f') # 2 \n"
"'3.14'\n"
"\n"
">>> repr(math.pi)\n"
"'3.141592653589793'"
#:
../../tutorial/floatingpoint.rst:107
msgid
""
"It's important to realize that this is, in a real sense, an illusion: you're "
"simply rounding the *display* of the true machine value."
msgstr
""
" ** "
""
#:
../../tutorial/floatingpoint.rst:110
msgid
""
"One illusion may beget another. For example, since 0.1 is not exactly 1/10, "
"summing three values of 0.1 may not yield exactly 0.3, either:"
msgstr
""
"0.1 1/10 "
"0.1 0.3 :"
#:
../../tutorial/floatingpoint.rst:113
msgid
""
">>> 0.1 + 0.1 + 0.1 == 0.3\n"
"False"
msgstr
""
">>> 0.1 + 0.1 + 0.1 == 0.3\n"
"False"
#:
../../tutorial/floatingpoint.rst:118
msgid
""
"Also, since the 0.1 cannot get any closer to the exact value of 1/10 and 0.3 "
"cannot get any closer to the exact value of 3/10, then pre-rounding with :"
"func:`round` function cannot help:"
msgstr
""
"0.1 1/10 0.3 3/10 "
" :func:`round` "
":"
#:
../../tutorial/floatingpoint.rst:122
msgid
""
">>> round(0.1, 1) + round(0.1, 1) + round(0.1, 1) == round(0.3, 1)\n"
"False"
msgstr
""
">>> round(0.1, 1) + round(0.1, 1) + round(0.1, 1) == round(0.3, 1)\n"
"False"
#:
../../tutorial/floatingpoint.rst:127
msgid
""
"Though the numbers cannot be made closer to their intended exact values, "
"the :func:`math.isclose` function can be useful for comparing inexact values:"
msgstr
""
""
" :func:`math.isclose` :"
#:
../../tutorial/floatingpoint.rst:130
msgid
""
">>> math.isclose(0.1 + 0.1 + 0.1, 0.3)\n"
"True"
msgstr
""
">>> math.isclose(0.1 + 0.1 + 0.1, 0.3)\n"
"True"
#:
../../tutorial/floatingpoint.rst:135
msgid
""
"Alternatively, the :func:`round` function can be used to compare rough "
"approximations:"
msgstr
" :func:`round` :"
#:
../../tutorial/floatingpoint.rst:138
msgid
""
">>> round(math.pi, ndigits=2) == round(22 / 7, ndigits=2)\n"
"True"
msgstr
""
">>> round(math.pi, ndigits=2) == round(22 / 7, ndigits=2)\n"
"True"
#:
../../tutorial/floatingpoint.rst:143
msgid
""
"Binary floating-point arithmetic holds many surprises like this. The "
"problem with
\"
0.1
\"
is explained in precise detail below, in the "
"
\"
Representation Error
\"
section. See `Examples of Floating Point Problems "
"<https://jvns.ca/blog/2023/01/13/examples-of-floating-point-problems/>`_ for "
"a pleasant summary of how binary floating point works and the kinds of "
"problems commonly encountered in practice. Also see `The Perils of Floating "
"Point <http://www.indowsway.com/floatingpoint.htm>`_ for a more complete "
"account of other common surprises."
msgstr
""
"2 0.1"
"2"
" `Examples of "
"Floating Point Problems <https://jvns.ca/blog/2023/01/13/examples-of-"
"floating-point-problems/>`_ "
" `The Perils of Floating Point <http://www.indowsway."
"com/floatingpoint.htm>`_ "
#:
../../tutorial/floatingpoint.rst:152
msgid
""
"As that says near the end,
\"
there are no easy answers.
\"
Still, don't be "
"unduly wary of floating point! The errors in Python float operations are "
"inherited from the floating-point hardware, and on most machines are on the "
"order of no more than 1 part in 2
\\
*
\\
*53 per operation. That's more than "
"adequate for most tasks, but you do need to keep in mind that it's not "
"decimal arithmetic and that every float operation can suffer a new rounding "
"error."
msgstr
""
""
"Python "
""
" 2
\\
*
\\
*53 1 "
"10 "
""
#:
../../tutorial/floatingpoint.rst:159
msgid
""
"While pathological cases do exist, for most casual use of floating-point "
"arithmetic you'll see the result you expect in the end if you simply round "
"the display of your final results to the number of decimal digits you "
"expect. :func:`str` usually suffices, and for finer control see the :meth:"
"`str.format` method's format specifiers in :ref:`formatstrings`."
msgstr
""
" 10 "
" :func:"
"`str` :ref:`formatstrings` :"
"meth:`str.format` "
#:
../../tutorial/floatingpoint.rst:165
msgid
""
"For use cases which require exact decimal representation, try using the :mod:"
"`decimal` module which implements decimal arithmetic suitable for accounting "
"applications and high-precision applications."
msgstr
""
"10 :mod:`decimal` "
""
"10"
#:
../../tutorial/floatingpoint.rst:169
msgid
""
"Another form of exact arithmetic is supported by the :mod:`fractions` module "
"which implements arithmetic based on rational numbers (so the numbers like "
"1/3 can be represented exactly)."
msgstr
""
" :mod:`fractions` "
" (1/3 )"
#:
../../tutorial/floatingpoint.rst:173
msgid
""
"If you are a heavy user of floating-point operations you should take a look "
"at the NumPy package and many other packages for mathematical and "
"statistical operations supplied by the SciPy project. See <https://scipy."
"org>."
msgstr
""
"NumPy SciPy "
" "
"<https://scipy.org> "
#:
../../tutorial/floatingpoint.rst:177
msgid
""
"Python provides tools that may help on those rare occasions when you really "
"*do* want to know the exact value of a float. The :meth:`float."
"as_integer_ratio` method expresses the value of a float as a fraction:"
msgstr
""
" ** "
"Python :meth:`float.as_integer_ratio` "
":"
#:
../../tutorial/floatingpoint.rst:182
msgid
""
">>> x = 3.14159\n"
">>> x.as_integer_ratio()\n"
"(3537115888337719, 1125899906842624)"
msgstr
""
">>> x = 3.14159\n"
">>> x.as_integer_ratio()\n"
"(3537115888337719, 1125899906842624)"
#:
../../tutorial/floatingpoint.rst:188
msgid
""
"Since the ratio is exact, it can be used to losslessly recreate the original "
"value:"
msgstr
":"
#:
../../tutorial/floatingpoint.rst:191
msgid
""
">>> x == 3537115888337719 / 1125899906842624\n"
"True"
msgstr
""
">>> x == 3537115888337719 / 1125899906842624\n"
"True"
#:
../../tutorial/floatingpoint.rst:196
msgid
""
"The :meth:`float.hex` method expresses a float in hexadecimal (base 16), "
"again giving the exact value stored by your computer:"
msgstr
""
":meth:`float.hex` float 16"
":"
#:
../../tutorial/floatingpoint.rst:199
msgid
""
">>> x.hex()\n"
"'0x1.921f9f01b866ep+1'"
msgstr
""
">>> x.hex()\n"
"'0x1.921f9f01b866ep+1'"
#:
../../tutorial/floatingpoint.rst:204
msgid
""
"This precise hexadecimal representation can be used to reconstruct the float "
"value exactly:"
msgstr
""
"16 float "
":"
#:
../../tutorial/floatingpoint.rst:207
msgid
""
">>> x == float.fromhex('0x1.921f9f01b866ep+1')\n"
"True"
msgstr
""
">>> x == float.fromhex('0x1.921f9f01b866ep+1')\n"
"True"
#:
../../tutorial/floatingpoint.rst:212
msgid
""
"Since the representation is exact, it is useful for reliably porting values "
"across different versions of Python (platform independence) and exchanging "
"data with other languages that support the same format (such as Java and "
"C99)."
msgstr
""
"16 () "
"Python "
"(Java C99 ) "
#:
../../tutorial/floatingpoint.rst:216
msgid
""
"Another helpful tool is the :func:`sum` function which helps mitigate loss-"
"of-precision during summation. It uses extended precision for intermediate "
"rounding steps as values are added onto a running total. That can make a "
"difference in overall accuracy so that the errors do not accumulate to the "
"point where they affect the final total:"
msgstr
""
" :func:`sum` "
""
":"
#:
../../tutorial/floatingpoint.rst:222
msgid
""
">>> 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 == 1.0\n"
"False\n"
">>> sum([0.1] * 10) == 1.0\n"
"True"
msgstr
""
">>> 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 == 1.0\n"
"False\n"
">>> sum([0.1] * 10) == 1.0\n"
"True"
#:
../../tutorial/floatingpoint.rst:229
msgid
""
"The :func:`math.fsum` goes further and tracks all of the
\"
lost digits
\"
as "
"values are added onto a running total so that the result has only a single "
"rounding. This is slower than :func:`sum` but will be more accurate in "
"uncommon cases where large magnitude inputs mostly cancel each other out "
"leaving a final sum near zero:"
msgstr
""
":func:`math.fsum` "
" :func:`sum` "
""
":"
#:
../../tutorial/floatingpoint.rst:235
msgid
""
">>> arr = [-0.10430216751806065, -266310978.67179024, 143401161448607.16,\n"
"... -143401161400469.7, 266262841.31058735, -0.003244936839808227]\n"
">>> float(sum(map(Fraction, arr))) # Exact summation with single rounding\n"
"8.042173697819788e-13\n"
">>> math.fsum(arr) # Single rounding\n"
"8.042173697819788e-13\n"
">>> sum(arr) # Multiple roundings in extended "
"precision\n"
"8.042178034628478e-13\n"
">>> total = 0.0\n"
">>> for x in arr:\n"
"... total += x # Multiple roundings in standard "
"precision\n"
"...\n"
">>> total # Straight addition has no correct "
"digits!\n"
"-0.0051575902860057365"
msgstr
""
">>> arr = [-0.10430216751806065, -266310978.67179024, 143401161448607.16,\n"
"... -143401161400469.7, 266262841.31058735, -0.003244936839808227]\n"
">>> float(sum(map(Fraction, arr))) # \n"
"8.042173697819788e-13\n"
">>> math.fsum(arr) # \n"
"8.042173697819788e-13\n"
">>> sum(arr) # \n"
"8.042178034628478e-13\n"
">>> total = 0.0\n"
">>> for x in arr:\n"
"... total += x # \n"
"...\n"
">>> total # \n"
"-0.0051575902860057365"
#:
../../tutorial/floatingpoint.rst:256
msgid
"Representation Error"
msgstr
""
msgid
""
"This section explains the
\"
0.1
\"
example in detail, and shows how you can "
"perform an exact analysis of cases like this yourself. Basic familiarity "
"with binary floating-point representation is assumed."
msgstr
""
"0.1"
"\n"
"2 "
#:
../../tutorial/floatingpoint.rst:262
msgid
""
":dfn:`Representation error` refers to the fact that some (most, actually) "
"decimal fractions cannot be represented exactly as binary (base 2) "
"fractions. This is the chief reason why Python (or Perl, C, C++, Java, "
"Fortran, and many others) often won't display the exact decimal number you "
"expect."
msgstr
""
" (:dfn:`Representation error`) () 10 "
" 2 Python ("
" PerlCC++JavaFortran ) 10 "
""
#:
../../tutorial/floatingpoint.rst:267
msgid
""
"Why is that? 1/10 is not exactly representable as a binary fraction. Since "
"at least 2000, almost all machines use IEEE 754 binary floating-point "
"arithmetic, and almost all platforms map Python floats to IEEE 754 binary64 "
"
\"
double precision
\"
values. IEEE 754 binary64 values contain 53 bits of "
"precision, so on input the computer strives to convert 0.1 to the closest "
"fraction it can of the form *J*/2**
\\
*N* where *J* is an integer containing "
"exactly 53 bits. Rewriting ::"
msgstr
""
"1/10 2 "
"2000 IEEE 754 2 "
" Python IEEE 754 binary64 "
"IEEE 754 binary64 53 "
"0.1 *J*/2**
\\
*N* "
" *J* 53 ::"
#:
../../tutorial/floatingpoint.rst:276
msgid
"1 / 10 ~= J / (2**N)"
msgstr
"1 / 10 ~= J / (2**N)"
#:
../../tutorial/floatingpoint.rst:278
msgid
"as ::"
msgstr
" ::"
#:
../../tutorial/floatingpoint.rst:280
msgid
"J ~= 2**N / 10"
msgstr
"J ~= 2**N / 10"
#:
../../tutorial/floatingpoint.rst:282
msgid
""
"and recalling that *J* has exactly 53 bits (is ``>= 2**52`` but ``< "
"2**53``), the best value for *N* is 56:"
msgstr
""
" *J* 53 (``>= 2**52`` ``< "
"2**53``) *N* 56 :"
#:
../../tutorial/floatingpoint.rst:285
msgid
""
">>> 2**52 <= 2**56 // 10 < 2**53\n"
"True"
msgstr
""
">>> 2**52 <= 2**56 // 10 < 2**53\n"
"True"
#:
../../tutorial/floatingpoint.rst:290
msgid
""
"That is, 56 is the only value for *N* that leaves *J* with exactly 53 bits. "
"The best possible value for *J* is then that quotient rounded:"
msgstr
""
" *J* 53 *N* 56 "
"*J* :"
#:
../../tutorial/floatingpoint.rst:293
msgid
""
">>> q, r = divmod(2**56, 10)\n"
">>> r\n"
"6"
msgstr
""
">>> q, r = divmod(2**56, 10)\n"
">>> r\n"
"6"
#:
../../tutorial/floatingpoint.rst:299
msgid
""
"Since the remainder is more than half of 10, the best approximation is "
"obtained by rounding up:"
msgstr
" 10 :"
#:
../../tutorial/floatingpoint.rst:302
msgid
""
">>> q+1\n"
"7205759403792794"
msgstr
""
">>> q+1\n"
"7205759403792794"
#:
../../tutorial/floatingpoint.rst:309
msgid
""
"Therefore the best possible approximation to 1/10 in IEEE 754 double "
"precision is::"
msgstr
"IEEE 754 1/10 ::"
#:
../../tutorial/floatingpoint.rst:312
msgid
"7205759403792794 / 2 ** 56"
msgstr
"7205759403792794 / 2 ** 56"
#:
../../tutorial/floatingpoint.rst:314
msgid
""
"Dividing both the numerator and denominator by two reduces the fraction to::"
msgstr
" 2 ::"
#:
../../tutorial/floatingpoint.rst:316
msgid
"3602879701896397 / 2 ** 55"
msgstr
"3602879701896397 / 2 ** 55"
#:
../../tutorial/floatingpoint.rst:318
msgid
""
"Note that since we rounded up, this is actually a little bit larger than "
"1/10; if we had not rounded up, the quotient would have been a little bit "
"smaller than 1/10. But in no case can it be *exactly* 1/10!"
msgstr
""
" 1/10 "
"\n"
" 1/10 "
" ** 1/10 "
#:
../../tutorial/floatingpoint.rst:322
msgid
""
"So the computer never
\"
sees
\"
1/10: what it sees is the exact fraction "
"given above, the best IEEE 754 double approximation it can get:"
msgstr
""
" 1/10 "
"IEEE 754 1/10 :"
#:
../../tutorial/floatingpoint.rst:325
msgid
""
">>> 0.1 * 2 ** 55\n"
"3602879701896397.0"
msgstr
""
">>> 0.1 * 2 ** 55\n"
"3602879701896397.0"
#:
../../tutorial/floatingpoint.rst:330
msgid
""
"If we multiply that fraction by 10
\\
*
\\
*55, we can see the value out to 55 "
"decimal digits:"
msgstr
""
" 10
\\
*
\\
*55 55 :"
#:
../../tutorial/floatingpoint.rst:333
msgid
""
">>> 3602879701896397 * 10 ** 55 // 2 ** 55\n"
"1000000000000000055511151231257827021181583404541015625"
msgstr
""
">>> 3602879701896397 * 10 ** 55 // 2 ** 55\n"
"1000000000000000055511151231257827021181583404541015625"
#:
../../tutorial/floatingpoint.rst:338
msgid
""
"meaning that the exact number stored in the computer is equal to the decimal "
"value 0.1000000000000000055511151231257827021181583404541015625. Instead of "
"displaying the full decimal value, many languages (including older versions "
"of Python), round the result to 17 significant digits:"
msgstr
""
"10 "
"0.1000000000000000055511151231257827021181583404541015625 "
" ( Python ) "
"10 17 :"
#:
../../tutorial/floatingpoint.rst:343
msgid
""
">>> format(0.1, '.17f')\n"
"'0.10000000000000001'"
msgstr
""
">>> format(0.1, '.17f')\n"
"'0.10000000000000001'"
#:
../../tutorial/floatingpoint.rst:348
msgid
""
"The :mod:`fractions` and :mod:`decimal` modules make these calculations easy:"
msgstr
""
":mod:`fractions` :mod:`decimal` "
":"
#:
../../tutorial/floatingpoint.rst:351
msgid
""
">>> from decimal import Decimal\n"
">>> from fractions import Fraction\n"
"\n"
">>> Fraction.from_float(0.1)\n"
"Fraction(3602879701896397, 36028797018963968)\n"
"\n"
">>> (0.1).as_integer_ratio()\n"
"(3602879701896397, 36028797018963968)\n"
"\n"
">>> Decimal.from_float(0.1)\n"
"Decimal('0.1000000000000000055511151231257827021181583404541015625')\n"
"\n"
">>> format(Decimal.from_float(0.1), '.17')\n"
"'0.10000000000000001'"
msgstr
""
">>> from decimal import Decimal\n"
">>> from fractions import Fraction\n"
"\n"
">>> Fraction.from_float(0.1)\n"
"Fraction(3602879701896397, 36028797018963968)\n"
"\n"
">>> (0.1).as_integer_ratio()\n"
"(3602879701896397, 36028797018963968)\n"
"\n"
">>> Decimal.from_float(0.1)\n"
"Decimal('0.1000000000000000055511151231257827021181583404541015625')\n"
"\n"
">>> format(Decimal.from_float(0.1), '.17')\n"
"'0.10000000000000001'"
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