It's also part of the modern perception that precision
is much greater than it is. A clock that reads hours
and minutes is accurate to around 30 seconds. A
clock that reads hours minutes and seconds is
accurate to 1/2 second.

You're confusing accuracy and resolution. You're also ignoring the fact that
the user can //see// when the minutes change. If you make sure the minutes
change at the same time your reference clock changes, the clock's accuracy
can be less than one second.


I've also seen it in ham radio where the frequency really
is around 14.200, but someone logs it as 14.203154
because that's what their (inacurate) receiver reads it as
and in computers where someone thinks floating
point numbers are integers. :-(

I don't think most digital communications receivers display the frequency
with a precision the LO is capable of.