The A above middle C on a piano is supposed to vibrate 440 times a second. That number is an international standard, agreed so that an oboe in Tashkent and a piano in Berlin can play the same note.
No string sits exactly on 440, and no tuner expects it to. The working rule in most workshops is that a note is acceptable if it is within one hertz of the standard — anywhere from 439 to 441.
Notice what that rule does not say. It does not say the note must be a little flat, or a little sharp. One hertz either way is close enough, because the ear does not care which side of 440 the string is on; it cares how far away it is.
A string measured at 442.5 hertz is two and a half hertz above the standard, which is outside the rule and clearly out of tune. A string at 439.2 is eight tenths below it, and passes.
The remarkable part is that a good tuner needs no meter to hear this. When two strings are close but not equal, the sound pulses — and the pulses come at exactly the rate of the difference. Two hertz apart gives two beats a second, one hertz apart gives one, and a string dead on the note gives none at all.
So the tuner is not guessing. She is counting a distance she can hear, and stopping when it falls below one.