The idea of using something like 45.734905° ± 0.000010° is that the information of the other digits is so small that it's better to ignore it. (Assuming that it is unbiases, and the other digits have some information at all.)
An intuitive way to understand this is considering how much work is necessary to extract information from the next digit. You can use statistic to extract more information. As a rule of thumb you need 100 times more measurements for each additional digit. So you need something like 100 (or 400) for the first digit, 10000 (or 40000) for the second digit and so on. (There is a constant here, I never remember the constant, perhaps it's 4, perhaps it's 1.)
To extract some information from the last 8 in 45.73490534578° you need 1000000000000 measurements! So it's better to just ignore the tiny amount of information in the 8.
In the lab in very controlled scenarios you can repeat a measurement very carefully a lot of times automatically and then use statistics. But if you have a handheld GPS, you can't repeat the measurement more than a few hundred of times.
A device that use a somewhat similar process is the https://en.wikipedia.org/wiki/Lock-in_amplifier it is not exactly this statistic trick, but note that it needs an stable environment to repeat the measurements. Wikipedia says that it can detect a signal 1 million times smaller than noise, but IIRC (the cheap ones?) can only detect a signal that is 1/100 or 1/1000 of the noise..
PS: Please never use 45.73490534578° (±0.00002°). If you use in a lab in the university, the TA will get mad at you. You can try using 45.73490534578° (±0.00002000000°) that is bad but not so horrible bad, the TA will still get mad at you but you may survive.