Postgresql – How does PotgreSQL round double precision numbers?

I understand how double precision works (exponent, mantissa, precision depending of the value, not exactly accurate numbers…) and I’m currently writing a blog post on this subject.
But when using it in PostgreSQL I found that PostgreSQL round these values.

The config parameter extra_float_digits=1 (or more) allows PostgreSQL to display every digits but this is not the case.

For instance : 1.1 can not be exactly stored in double precision, it is approximated as 1.100000000000000088817841970012523233890533447265625 because this is the closest value that can be stored. The previous/next step is far from 2,2204460492 × 10^−16
Why this stored number can not be visualised ?

I think that the code is rounding the number to 10^-15 because this is the max precision you can have for this order of magnitude but I can not confirm this.

I have three questions :

1. Does PostgreSQL round the value ?
2. Is it possible to have the exact value stored ?
3. Is it already the case but I make some mistakes (I’m using PSQL) ?

I set :

SET extra_float_digits=3;

I try

SELECT 1.1::float8;
 float8
--------
    1.1

The result is 1.1 which is not the exact stored value.
The same for :

SELECT 1.1::float8::varchar;
 varchar
---------
 1.1

If I try with the exact value :

SELECT 1.100000000000000088817841970012523233890533447265625::float8;
 float8
--------
    1.1