Why does 0.125, formatted with 2 digits of decimal precision, show "0.12" not "0.13"?

Consider:

#include <iostream>
#include <iomanip>
 
int main()
{
    std::cout << std::fixed << std::setprecision(2);
    std::cout << 0.125 << '\n'; // Prints "0.12"
    std::cout << 0.126 << '\n'; // Prints "0.13" as expected
}

Demo

I know that floating point math isn't perfectly precise, but isn't 0.125 one of the values that actually is represented exactly? Why does it round down to "0.12" instead of up to "0.13" when formatting it?