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# round() function python

why does round(4.5) return 4? why does round(-4.5) return -4? MOD

Good question-- round() will round a value to the "nearest" integer. But if you are on the "knife's edge" of the rounding point you can get what seems like unpredictable results.

Visit this link for further details (14. Floating Point Arithmetic: Issues and Limitations):

https://docs.python.org/2/tutorial/floatingpoint.html

Consider the following program where we refine a string and convert it to floating point. This program will explore the limits of the string format() method as well as float() type cast and round()

```# start with a string representation of x
x = '4.49'
# loop keeps adding nines to the end of a string
# e.g. 4.49, 4.499, 4.4999, etc.
for _ in range(100):
x = x + '9'
print 'x = "{}"'.format(x)
print 'float(x) = {}'.format(float(x))
print 'round(float(x)) = {}'.format(round(float(x)))
```

Ok... here is the seemingly abberant behavior as we approach 4.5. I am using a 32 bit Python 2.7. Your results will be a little different with a 64 bit python, but there will be a "crossover" point as I show below.

```# note the float value is not quite 4.5
x = "4.49999999999"
float(x) = 4.49999999999
round(float(x)) = 4.0
# but now the float value becomes 4.5, but it still rounds to 4.0
x = "4.499999999999"
float(x) = 4.5
round(float(x)) = 4.0
x = "4.4999999999999"
float(x) = 4.5
round(float(x)) = 4.0
x = "4.49999999999999"
float(x) = 4.5
round(float(x)) = 4.0
x = "4.499999999999999"
float(x) = 4.5
round(float(x)) = 4.0
# at this point, the rounding of our 4.5 changes to 5.0 here
x = "4.4999999999999999"
float(x) = 4.5
round(float(x)) = 5.0
x = "4.49999999999999999"
float(x) = 4.5
round(float(x)) = 5.0
```

I read the document that you linked to your response and i read that this problem only really happens to decimal fractions. "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."