Python float to int conversion

Question

Basically, I'm converting a float to an int, but I don't always have the expected value.

Here's the code I'm executing:

x = 2.51

print("--------- 251.0") y = 251.0 print(y) print(int(y))  print("--------- 2.51 * 100") y = x * 100 print(y) print(int(y))  print("--------- 2.51 * 1000 / 10") y = x * 1000 / 10 print(y) print(int(y))  print("--------- 2.51 * 100 * 10 / 10") y = x * 100 * 10 / 10 print(y) print(int(y))  x = 4.02 print("--------- 402.0") y = 402.0 print(y) print(int(y))  print("--------- 4.02 * 100") y = x * 100 print(y) print(int(y))  print("--------- 4.02 * 1000 / 10") y = x * 1000 / 10 print(y) print(int(y))  print("--------- 4.02 * 100 * 10 / 10") y = x * 100 * 10 / 10 print(y) print(int(y)) 

And here's the result (first value is the result of the operation, second value is int() of the same operation):

--------- 251.0 251.0 251 --------- 2.51 * 100 251.0 250 --------- 2.51 * 1000 / 10 251.0 251 --------- 2.51 * 100 * 10 / 10 251.0 250 --------- 402.0 402.0 402 --------- 4.02 * 100 402.0 401 --------- 4.02 * 1000 / 10 402.0 401 --------- 4.02 * 100 * 10 / 10 402.0 401 

2.51 and 4.02 are the only values that lead to that strange behaviour on the 2.50 -> 5.00 range. Every other two digits value in that range converts to int without any problem when given the same operations.

So, what am I missing that leads to those results? I'm using Python 2.7.2 by the way.

Answer 1

2.51 * 100 = 250.999999999997 

The int() function simply truncates the number at the decimal point, giving 250. Use

int(round(2.51*100))  

to get 251 as an integer. In general, floating point numbers cannot be represented exactly. One should therefore be careful of round-off errors. As mentioned, this is not a Python-specific problem. It's a recurring problem in all computer languages.

Answer 2

What Every Computer Scientist Should Know About Floating-Point Arithmetic

Floating-point numbers cannot represent all the numbers. In particular, 2.51 cannot be represented by a floating-point number, and is represented by a number very close to it:

>>> print "%.16f" % 2.51 2.5099999999999998 >>> 2.51*100 250.99999999999997 >>> 4.02*100 401.99999999999994 

If you use int, which truncates the numbers, you get:

250 401 

Have a look at the Decimal type.