Rather than thinking in terms of sig figs, the smart approach is to think in terms of _uncertainty_ which in turn can be formalized in terms of probability distributions.
As pointed out by von Neumann among others, there is no such thing as a random number.
If it's random, it's not a number.
If it's a number, it's not random.
You can have a random distribution over numbers, but in that case the randomness is in the distribution, not in some number that may have been drawn from such a distribution.
One of the most disastrous aspects of the "sig figs" dogma is that it tramples on this distinction.
Many of the numbers that we encounter in physics are just plain numbers, not distributions. The "sig figs" dogma requires students to attribute an uncertainty to every number that they read or write, which is just plain wrong, profoundly wrong.
Specific constructive suggestion: in cases when you are talking about a distribution _and_ the distribution can be parameterized by a central value and a width, write these two quantities separately and explicitly, perhaps in the form 543 ± 21.
Conversely: When writing, do not use "sig figs" for anything, ever. Do not try to use one numeral to represent two numbers. When reading, do not interpret the number of digits as implying anything about the uncertainty, much less the significance.
See item #101 for a catalog of related issues.
Rather than thinking in terms of sig figs, the smart approach is to think in terms of _uncertainty_ which in turn can be formalized in terms of probability distributions.
As pointed out by von Neumann among others, there is no such thing as a random number.
One of the most disastrous aspects of the "sig figs" dogma is that it tramples on this distinction.
Many of the numbers that we encounter in physics are just plain numbers, not distributions. The "sig figs" dogma requires students to attribute an uncertainty to every number that they read or write, which is just plain wrong, profoundly wrong.
Specific constructive suggestion: in cases when you are talking about a distribution _and_ the distribution can be parameterized by a central value and a width, write these two quantities separately and explicitly, perhaps in the form 543 ± 21.
Conversely: When writing, do not use "sig figs" for anything, ever. Do not try to use one numeral to represent two numbers. When reading, do not interpret the number of digits as implying anything about the uncertainty, much less the significance.