Python 3 semantics for integer division

As I refresh my skills in Python 2 to Python 3 semantics I discovered there is a difference in the division operator (i.e. /).

When using integers in Python 2 the result (by default) is an integer. For example.

$ python2
Python 2.7.6 (default, Mar 22 2014, 22:59:56)
>>> 1/2
0
>>> 1/2.0
0.5

In Python 3 the result is a float.

$ python3
Python 3.4.0 (default, Apr 11 2014, 13:05:11)
>>> 1/2
0.5

It has been encouraged in the Porting Python 2 Code to Python 3 documentation to perform the following import.

$ python2
Python 2.7.6 (default, Mar 22 2014, 22:59:56)
>>> from __future__ import division
>>> 1/2
0.5

I was also unaware of the floor operator (i.e. //) as specified in PEP 238 .

$ python2
Python 2.7.6 (default, Mar 22 2014, 22:59:56)
>>> from __future__ import division
>>> 1//2
0
>>> 1/2
0.5

I uncovered this by playing with algorithms between versions. This Newton Method for the Square Root was something I was unaware of, and this example failed when using Python 2.

My improved version on the referenced example without an import.

def squareroot(number, precision = 5):
  root = number/2.0
  for i in range(20):
    nroot = (1/2.0)*(root + (number / root))
    #print i, nroot
    if (root - nroot < 1.0/10**precision):
      break
    root = nroot
  return round(nroot, precision)

>>> squareroot(10)
3.16228
>>> squareroot(10,1)
3.2
>>> squareroot(10,2)
3.16
>>> squareroot(10,5)
3.16228
>>> squareroot(10,10)
3.1622776602