Is 17-digit decimal representation of float in Python 3 (using IEEE-754) always "exact" up to numerical accuracy?

Is the following true for all float numbers r from 0 to 1 in CPython 3.10 or newer that uses IEEE-754 floating-point numbers?

float('%.17g' % r) == r

In other words, is 17-digit decimal representation of float numbers from 0 to 1 accurate enough to be equal to their binary counterparts?

My conjecture is that it is true for 17 digits (but not 16), as I did not find a counterexample yet with the following program:

import random

def check(precision=17):
  r = random.random()
  d = float(f'%.{precision}g' % r) - r
  if d != 0:
    print(d)

for i in range(1000000000):
  check(17)

However, this does not cover all cases, so I am searching for an answer grounded in theory.

Depending on the answer, I am searching for the answer to the following quesitons:

• Would it be true for all float numbers?
• If the conjecture is not true for 17 digits, is it true for more?
• If the conjecture is not true, is at least each float('%.17f' % r) unique?