None of these calculations are going to work out exactly.  Look-up "what
every computer scientist needs to know about floating point" and see the
floating-point appendix in the Python tutorial.  In this case, the
difference is only one bit in the last place:

  >>> 0.70710678118654746.hex()
  '0x1.6a09e667f3bccp-1'
  >>> 0.70710678118654757.hex()
  '0x1.6a09e667f3bcdp-1'