The number of registered voters in Hennepin County in the last election was 729,527.

Presuming that this statistic is based on an official database, it is precise by definition
for a particular time and place. This number is accurate to 6 significant figures.

The city of St. Paul has a population of 285,068.

This statement is not likely to be correct. Even if a city's population could be defined
in a precise way (permanent residents? homeless? warm bodies?), how can we account for the
minute by minute changes that occur as people move in and out, or are born and die?

It is entirely possible that the last census yielded precisely 285,068 records, and this may be
the population for legal purposes, but it is highly unlikely that this is the true population.
To better reflect this fact, one might list the population as 284,000 or even 290,000. These two quantities
have been rounded off to three and two significant figures respectively and have the following meanings:

• 284,000 - implies that the population is believed to be within the range of
283,500 to 284,500 (or 284,000±500). This number is accurate to 3 significant figures.

• 290,000 - implies that the population is believed to be within the range of
285,000 to 295,000 (or 290,000±5,000). This number is accurate to 2 significant figures.

Which of these numbers is chosen depends on the degree of confidence we have in the original
census figure, how long ago the census was conducted, migration trends, and a host of other considerations.

The point this exercise is that the concept of significant digits has less to do
with mathematics than with our confidence in a particular measurement.