EOL - 1 month ago 15
Python Question

# Integer division compared to floored quotient: why this surprising result?

The

`//`
"integer division" operator of Python surprised me, today:

``````>>> math.floor(11/1.1)
10.0
>>> 11//1.1
9.0
``````

The documentation reads "(floored) quotient of x and y". So, why is math.floor(11/1.1) equal to 10, but 11//1.1 equal to 9?

Because 1.1 can't be represented in binary form exactly; the approximation is a littler higher than 1.1 - therefore the division result is a bit too small.

Try the following:

Under Python 2, type at the console:

``````>>> 1.1
1.1000000000000001
``````

In Python 3.1, the console will display `1.1`, but internally, it's still the same number.

But:

``````>>> 11/1.1
10.0
``````

As gnibbler points out, this is the result of "internal rounding" within the available precision limits of floats. And as The MYYN points out in his comment, `//` uses a different algorithm to calculate the floor division result than `math.floor()` in order to preserve `a == (a//b)*b + a%b` as well as possible.

Use the `Decimal` type if you need this precision.