Why does the Python 3 string function appear to reduce precision of float?

Question

In a Python (3.6.7) interactive shell on Ubuntu 18, both

>>> n = str(3.140000000000000124344978758017532527446746826171875)
>>> print(n)

and

>>> print(3.140000000000000124344978758017532527446746826171875)

yield 3.14. While

>>> print('3.140000000000000124344978758017532527446746826171875')

yields 3.140000000000000124344978758017532527446746826171875

Why is this?

Note; I am not asking why floating-point numbers lose precision, but specifically, why the use of str(n) and 'n' (quotes) behave differently with print().

Answer 1

In case 1 and 2, what you manipulate is a float object

f = 3.140000000000000124344978758017532527446746826171875

# In case 1
print(str(f))

# In case 2
print(f)

And str(f) converts the float object to a string, print(f) means print(repr(f)), repr(f) also converts the float object to a string.

In case 3, what you manipulate is a string object which contains 53 characters,

What happened when convert a float object to a string?

str(f) and repr(f) call the same function float_repr.

In function float_repr, if you haven't specify precision parameter, a float object will be convert to string with double-precision floating-point format.

Double-precision floating-point format gives from 15 to 17 significant decimal digits precision.

So in this case, significant decimal digits precision is 16, 3.140000000000000124344978758017532527446746826171875 will be converted to 3.140000000000000.

An clearer example:

>>> str(3.140000000000000123)
'3.14'

>>> str(3.14000000000000123)
'3.140000000000001'

>>> print(3.14000000000000123)
3.140000000000001