Python浮动比率

Python float to ratio(Python浮动比率)

问题描述

我尝试获取变量的比例并得到意想不到的结果.有人可以解释一下吗?

I try get ration of variable and get unexpected result. Can somebody explain this?

>>> value = 3.2
>>> ratios = value.as_integer_ratio()
>>> ratios
(3602879701896397, 1125899906842624)
>>> ratios[0] / ratios[1]
3.2

>>> value = 2.5
>>> value.as_integer_ratio()
(5, 2)

>>> from fractions import Fraction
>>> Fraction(3.2)
Fraction(3602879701896397, 1125899906842624)
>>> Fraction(3.2).limit_denominator()
Fraction(16, 5)

来自 Fraction.limit_denominator() 函数一个>:

From the Fraction.limit_denominator() function:

查找并返回与 self 最接近且分母最多为 max_denominator 的 Fraction.此方法对于找到给定浮点数的有理逼近很有用

Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number

浮点数精度有限，不能精确表示；你看到的是一个四舍五入的表示，但实数是:

Floating point numbers are limited in precision and cannot represent many numbers exactly; what you see is a rounded representation, but the real number is:

>>> format(3.2, '.50f')
'3.20000000000000017763568394002504646778106689453125'

因为浮点数表示为二进制小数的总和；1/5 只能通过将 1/8 + 1/16 + 1/128 + 更多的二进制分数相加来表示，以增加 2 的指数.

because a floating point number is represented as a sum of binary fractions; 1/5 can only be represented by adding up 1/8 + 1/16 + 1/128 + more binary fractions for increasing exponents of two.

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