为什么 Python 中这两个被证明相等的小数中有一些被认为不相等？

Question

在我的 Python 课程中，我正在尝试比较将多个浮点数相加与将多个小数相加的准确性。实验室的要求之一是计算有多少次将 .1 相加得到正确的和。我的代码中的所有内容都正常工作，除了我的计数器，用于计算 decimal 添加的正确数量。对于 100 次迭代，它只计算 20 次是正确的（每 5 次迭代），尽管我已经通过打印每次迭代证明它们都是正确的。为什么会发生这种情况，如何解决？谢谢。 （您可以在下面找到完整的代码以获得完整的上下文和输出。）

代码：

from decimal import *

floatSum = 0
decSum = 0
toAddFloat = .1
toAddDec = Decimal(".1")
max = 100 # number of iterations
floatCorrect = 0
decCorrect = 0

# continually add .1 as floats together for specified number of iterations
for i in range (0, max, 1):
    floatSum = floatSum + toAddFloat
    print(floatSum,(i + 1) / 10)
    if (floatSum == (i + 1) / 10): # check if the addition is what it should be
        floatCorrect += 1

i = 0

# continually add .1 as decimals together for specified number of iterations
for i in range (0, max, 1):
    decSum = decSum + toAddDec
    print(decSum, (i + 1) / 10)
    print(decCorrect)
    if (decSum == (i + 1) / 10): # check if the addition is what it should be
        decCorrect += 1

print("\nFLOAT RESULTS:")
print("--------------")
print("Iterations: ", max, ", Added Number: ", toAddFloat, ", Calculated Sum: ", floatSum,
        ", Times Correct: ", floatCorrect, ", Correct Result: ", toAddFloat * max, ", Difference: ", (toAddFloat * max) - floatSum, "\n")

print("DECIMAL RESULTS:")
print("----------------")
print("Iterations: ", max, ", Added Number: ", toAddDec, ", Calculated Sum: ", decSum, 
        ", Times Correct: ", decCorrect, ", Correct Result: ", toAddDec * max, ", Difference: ", (toAddDec * max) - decSum)

（部分） 输出：

FLOAT RESULTS:
--------------
Iterations:  100 , Added Number:  0.1 , Calculated Sum:  9.99999999999998 , Times Correct:  11 , Correct Result:  10.0 , Difference:  1.9539925233402755e-14

DECIMAL RESULTS:
----------------
Iterations:  100 , Added Number:  0.1 , Calculated Sum:  10.0 , Times Correct:  20 , Correct Result:  10.0 , Difference:  0.0

Answer 1

将此行更新为

 if (decSum*10 == (i + 1)):

for python 除法给出浮点数结果。如果这个数字没有像它看起来的那样精确表示，它不会等于小数对应的数字。

为什么 Python 中这两个被证明相等的小数中有一些被认为不相等？

Why are some of these two proven-to-be-equal decimals in Python considered not to be equal?

python

floating-point

decimal

precision

equality