system
Given the following post, respond as if you're commenting on Reddit:
human
How was Millikan able to calculate the charge of an electron so precisely?

I can't wrap my head around how he was able to calculate a value for charge in the neighborhood of 10^-19 using such a crude measurement system.  Anything could have impacted the measurements, from his own fatigue in eyeballing the oil drop motion and size, to slight variations in the content of the air in the system, to the vibrations of the apparatus, to his electrical measurements being imprecise due to effects like resistive heating or voltage fluctuations.  

I suppose all these could be made to be less impactful by measuring more drops, OR by the charge amount on each drop being a relatively small integer, but I'm having trouble wrapping my head around the precision he was able to achieve with his experiment.  (I realize he was off by something like 2%, that still doesn't change the fact that we're talking about quantities in the 10^-19 range)

I must be looking at this the wrong way, can anyone help me?
gpt
The fact that we are talking about 1E-19 range is largely irrelevant. 

He had 4 significant figures in his result (the result he reported in his Nobel lecture was 4.774(5)E-10 statC). Since he was off by 2%, that tells you that he really only had 2 significant figures. 

You are right about what all could have affected his measurements, but if you consider that he had 2 significant figures, this comes down to "how was he able to measure his parameters down to 2 significant figures", and to answer that, you need to consider what his parameters were:

 * Density of oil: not a big deal to measure to 2 significant figures macroscopically
 * Density of air: likewise
 * Gravitational acceleration: likewise
 * Droplet radius: doable with microscopes of the time; also, because droplets are spherical at that scale, not affected by droplet movement or observer movement.
 * Droplet speed: you measure transit time across a known distance in the field of view of the microscope, so you need a ruler that's good to 2 significant figures on the scale of the microscope he was using, and the ability to measure time to 2 decimal places. The ruler was doable with his technology, and time measurements were not an issue because his droplets were moving slowly
 * Voltage between the plates: no problem measuring that to 2 decimal places in kilovolt range (which is what he was using) with technology of the time

Edit: most of the 19 decimal points in his result come from droplet volume, so from cubing the radius of a droplet. If you can measure radius to ±1E-6m, you can measure volume to ±1E-18m^3 . Measuring down to a micron was well within the microscope technology of the time.