why 1 // 0.05 results in 19.0 in python?

Question

I'm a new to python and I found a confusing result when using Python3.5.1 on my mac, I simply ran this command in my terminal

    1 // 0.05

However, it printed 19.0 on my screen. From my point of view, it should be 20. Can someone explain what's happening here? I've already known that the '//' is similar to the math.floor() function. But I still can't get across to this.

Answer 1

Because the Python floating-point literal 0.05 represents a number very slightly larger than the mathematical value 0.05.

>>> '%.60f' % 0.05
'0.050000000000000002775557561562891351059079170227050781250000'

// is floor division, meaning that the result is the largest integer n such that n times the divisor is less than or equal to the dividend. Since 20 times 0.05000000000000000277555756156289135105907917022705078125 is larger than 1, this means the correct result is 19.

As for why the Python literal 0.05 doesn't represent the number 0.05, as well as many other things about floating point, see What Every Computer Scientist Should Know About Floating-Point Arithmetic

Answer 2

0.05 is not exactly representable in floating point. "%0.20f" % 0.05 shows that 0.05 is stored as a value very slightly greater than the exact value:

>>> print "%0.20f" % 0.05
0.05000000000000000278

On the other hand 1/0.05 does appear to be exactly 20:

>>> print "%0.20f" % (1/0.05)
20.00000000000000000000

However all floating point values are rounded to double when stored but calculations are done to a higher precision. In this case it seems the floor operation performed by 1//0.05 is done at full internal precision hence it is rounded down.