Alright, if "you" have only ever used python. In C, for example, we have hexadecimal floating point literals that represent all floats and doubles exactly (including infinities and nans that make the json parser fail miserably).
How do you do that?
A couple of resources I found but which I’m not sure if are about exactly what you speak of
https://stackoverflow.com/questions/65480947/is-ieee-754-rep...
https://gcc.gnu.org/onlinedocs/gcc/Hex-Floats.html
Furthermore, what exactly do you mean by “all floats and doubles exactly”?
// define a floating-point literal in hex and print it in decimal
float x = 0x1p-8; // x = 1.0/256
printf("x = %g\n", x); // prints 0.00390625
// define a floating point literal in decimal and print it in various ways
float y = 0.3; // non-representable, rounded to closest float
printf("y = %g\n", y); // 0.3 (the %g format does some heuristics)
printf("y = %.10f\n", y); // 0.3000000119
printf("y = %.20f\n", y); // 0.30000001192092895508
printf("y = %a\n", f); // 0x1.333334p-2100000.000000000017
And then you print it.
Does it preserve the exact value?
If you print your variable with the %a format, then YES, the exact value is preserved and there is no loss of information. The problem is that the literal that you wrote cannot be represented exactly. But this is hardly a fault of the floats. Ints have exactly the same problem:
int x = 2.5; // x gets the value 2
int y = 7/3; // same thing