fractions — 分數 · Python3.7.3官方文檔簡體中文

### 導航 - [索引](../genindex.xhtml "總目錄") - [模塊](../py-modindex.xhtml "Python 模塊索引") | - [下一頁](random.xhtml "random --- 生成偽隨機數") | - [上一頁](decimal.xhtml "decimal --- 十進制定點和浮點運算") | - ![](https://box.kancloud.cn/a721fc7ec672275e257bbbfde49a4d4e_16x16.png) - [Python](https://www.python.org/) ? - zh\_CN 3.7.3 [文檔](../index.xhtml) ? - [Python 標準庫](index.xhtml) ? - [數字和數學模塊](numeric.xhtml) ? - $('.inline-search').show(0); | # [`fractions`](#module-fractions "fractions: Rational numbers.") --- 分數 **源代碼** [Lib/fractions.py](https://github.com/python/cpython/tree/3.7/Lib/fractions.py) \[https://github.com/python/cpython/tree/3.7/Lib/fractions.py\] - - - - - - [`fractions`](#module-fractions "fractions: Rational numbers.") 模塊支持分數運算。分數實例可以由一對整數，一個分數，或者一個字符串構建而成。 *class* `fractions.``Fraction`(*numerator=0*, *denominator=1*)*class* `fractions.``Fraction`(*other\_fraction*)*class* `fractions.``Fraction`(*float*)*class* `fractions.``Fraction`(*decimal*)*class* `fractions.``Fraction`(*string*)The first version requires that *numerator* and *denominator* are instances of [`numbers.Rational`](numbers.xhtml#numbers.Rational "numbers.Rational") and returns a new [`Fraction`](#fractions.Fraction "fractions.Fraction") instance with value `numerator/denominator`. If *denominator* is `0`, it raises a [`ZeroDivisionError`](exceptions.xhtml#ZeroDivisionError "ZeroDivisionError"). The second version requires that *other\_fraction* is an instance of [`numbers.Rational`](numbers.xhtml#numbers.Rational "numbers.Rational") and returns a [`Fraction`](#fractions.Fraction "fractions.Fraction") instance with the same value. The next two versions accept either a [`float`](functions.xhtml#float "float") or a [`decimal.Decimal`](decimal.xhtml#decimal.Decimal "decimal.Decimal") instance, and return a [`Fraction`](#fractions.Fraction "fractions.Fraction") instance with exactly the same value. Note that due to the usual issues with binary floating-point (see [浮點算術：爭議和限制](../tutorial/floatingpoint.xhtml#tut-fp-issues)), the argument to `Fraction(1.1)` is not exactly equal to 11/10, and so `Fraction(1.1)` does *not* return `Fraction(11, 10)` as one might expect. (But see the documentation for the [`limit_denominator()`](#fractions.Fraction.limit_denominator "fractions.Fraction.limit_denominator") method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is: ``` [sign] numerator ['/' denominator] ``` where the optional `sign` may be either '+' or '-' and `numerator` and `denominator` (if present) are strings of decimal digits. In addition, any string that represents a finite value and is accepted by the [`float`](functions.xhtml#float "float") constructor is also accepted by the [`Fraction`](#fractions.Fraction "fractions.Fraction") constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples: ``` >>> from fractions import Fraction >>> Fraction(16, -10) Fraction(-8, 5) >>> Fraction(123) Fraction(123, 1) >>> Fraction() Fraction(0, 1) >>> Fraction('3/7') Fraction(3, 7) >>> Fraction(' -3/7 ') Fraction(-3, 7) >>> Fraction('1.414213 \t\n') Fraction(1414213, 1000000) >>> Fraction('-.125') Fraction(-1, 8) >>> Fraction('7e-6') Fraction(7, 1000000) >>> Fraction(2.25) Fraction(9, 4) >>> Fraction(1.1) Fraction(2476979795053773, 2251799813685248) >>> from decimal import Decimal >>> Fraction(Decimal('1.1')) Fraction(11, 10) ``` The [`Fraction`](#fractions.Fraction "fractions.Fraction") class inherits from the abstract base class [`numbers.Rational`](numbers.xhtml#numbers.Rational "numbers.Rational"), and implements all of the methods and operations from that class. [`Fraction`](#fractions.Fraction "fractions.Fraction") instances are hashable, and should be treated as immutable. In addition, [`Fraction`](#fractions.Fraction "fractions.Fraction") has the following properties and methods: 在 3.2 版更改: The [`Fraction`](#fractions.Fraction "fractions.Fraction") constructor now accepts [`float`](functions.xhtml#float "float") and [`decimal.Decimal`](decimal.xhtml#decimal.Decimal "decimal.Decimal") instances. `numerator`最簡分數形式的分子。 `denominator`最簡分數形式的分母。 `from_float`(*flt*)This class method constructs a [`Fraction`](#fractions.Fraction "fractions.Fraction") representing the exact value of *flt*, which must be a [`float`](functions.xhtml#float "float"). Beware that `Fraction.from_float(0.3)` is not the same value as `Fraction(3, 10)`. 注解 From Python 3.2 onwards, you can also construct a [`Fraction`](#fractions.Fraction "fractions.Fraction") instance directly from a [`float`](functions.xhtml#float "float"). `from_decimal`(*dec*)This class method constructs a [`Fraction`](#fractions.Fraction "fractions.Fraction") representing the exact value of *dec*, which must be a [`decimal.Decimal`](decimal.xhtml#decimal.Decimal "decimal.Decimal") instance. 注解 From Python 3.2 onwards, you can also construct a [`Fraction`](#fractions.Fraction "fractions.Fraction") instance directly from a [`decimal.Decimal`](decimal.xhtml#decimal.Decimal "decimal.Decimal")instance. `limit_denominator`(*max\_denominator=1000000*)Finds and returns the closest [`Fraction`](#fractions.Fraction "fractions.Fraction") to `self` that has denominator at most max\_denominator. This method is useful for finding rational approximations to a given floating-point number: ``` >>> from fractions import Fraction >>> Fraction('3.1415926535897932').limit_denominator(1000) Fraction(355, 113) ``` or for recovering a rational number that's represented as a float: ``` >>> from math import pi, cos >>> Fraction(cos(pi/3)) Fraction(4503599627370497, 9007199254740992) >>> Fraction(cos(pi/3)).limit_denominator() Fraction(1, 2) >>> Fraction(1.1).limit_denominator() Fraction(11, 10) ``` `__floor__`()Returns the greatest [`int`](functions.xhtml#int "int")`<= self`. This method can also be accessed through the [`math.floor()`](math.xhtml#math.floor "math.floor") function: ``` >>> from math import floor >>> floor(Fraction(355, 113)) 3 ``` `__ceil__`()Returns the least [`int`](functions.xhtml#int "int")`>= self`. This method can also be accessed through the [`math.ceil()`](math.xhtml#math.ceil "math.ceil") function. `__round__`()`__round__`(*ndigits*)The first version returns the nearest [`int`](functions.xhtml#int "int") to `self`, rounding half to even. The second version rounds `self` to the nearest multiple of `Fraction(1, 10**ndigits)` (logically, if `ndigits` is negative), again rounding half toward even. This method can also be accessed through the [`round()`](functions.xhtml#round "round") function. `fractions.``gcd`(*a*, *b*)返回整數 *a* 和 *b* 的最大公約數。如果 *a* 或 *b* 之一非零，則 `gcd(a, b)` 的絕對值是能同時整除 *a* 和 *b* 的最大整數。若 *b* 非零，則 `gcd(a,b)` 與 *b* 同號；否則返回值與 *a* 同號。`gcd(0, 0)` 返回 `0`。 3\.5 版后已移除: 由 [`math.gcd()`](math.xhtml#math.gcd "math.gcd") 取代. 參見 [`numbers`](numbers.xhtml#module-numbers "numbers: Numeric abstract base classes (Complex, Real, Integral, etc.).") 模塊The abstract base classes making up the numeric tower. ### 導航 - [索引](../genindex.xhtml "總目錄") - [模塊](../py-modindex.xhtml "Python 模塊索引") | - [下一頁](random.xhtml "random --- 生成偽隨機數") | - [上一頁](decimal.xhtml "decimal --- 十進制定點和浮點運算") | - ![](https://box.kancloud.cn/a721fc7ec672275e257bbbfde49a4d4e_16x16.png) - [Python](https://www.python.org/) ? - zh\_CN 3.7.3 [文檔](../index.xhtml) ? - [Python 標準庫](index.xhtml) ? - [數字和數學模塊](numeric.xhtml) ? - $('.inline-search').show(0); | ? [版權所有](../copyright.xhtml) 2001-2019, Python Software Foundation. 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