Because if you forget to write down as many digits as you can know from the measurement, you are denying the data recipient access to all the available data.
BUT, if you write down TOO MANY DIGITS, beyond the digits available from the measurement method, all the digits beyond the proper number of significant digits are simply FICTIONAL DIGITS. You don't actually know their values, therefore you shouldn't report them.
Digits that will appear to "flicker" on a digital measurement device are those that are fiction, for which you should cease writing down digits. Those are digits that the measurement device cannot accurately measure.
On an analog measurement device, it depends on (1) how tightly the display was calibrated, and (2) how closely your eyes can read the transition between marked ticks.
BUT, if you write down TOO MANY DIGITS, beyond the digits available from the measurement method, all the digits beyond the proper number of significant digits are simply FICTIONAL DIGITS. You don't actually know their values, therefore you shouldn't report them.
Digits that will appear to "flicker" on a digital measurement device are those that are fiction, for which you should cease writing down digits. Those are digits that the measurement device cannot accurately measure.
On an analog measurement device, it depends on (1) how tightly the display was calibrated, and (2) how closely your eyes can read the transition between marked ticks.