python - 如何确定小数是否可以完全表示为 Python float？

Question

来自 Python tutorial :

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.

我想知道如何检查给定的小数是否会精确表示为 Python float。例如，0.25 可以精确表示，而 0.1 不能:

>>> 0.1 + 0.1 + 0.1 == 0.3
False
>>> 0.25 + 0.25 + 0.25 == 0.75
True

Answer 1

在那个页面上:

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.

因此，要使小数精确表示为 float，它必须是分母为 2 的幂的分数:

>>> 1/10 + 1/10 + 1/10 == 3/10  # 0.1 + 0.1 + 0.1
False
>>> 1/4 + 1/4 + 1/4 == 3/4      # 0.25 + 0.25 + 0.25
True