I wonder... without an electric tuner how do you tell if the note is tuned?
There is the reference pitch, you tune to the fork. Then you tune what is called the temperament octave using the reference pitch as a starting point. There are different methods of setting the temperament, it's personal preference. Because we use equal temperament, none of the intervals except unisons and octaves are tuned pure. You tune the rest of the piano in octaves using the temperament octave as reference.
There are electronic tuners that professionals use specifically for pianos, but they aren't the chepie ones. They care designed to account for inharmonicity so you don't go tuning the piano out of tune with itself. EG:
https://www.concentric.net/~Fast440/atm/atm.html