Check out the documentation from Swift's Piksi receiver project for a good introduction to existing technology:
https://www.swiftnav.com/sites/default/files/whitepapers/loc...
The technology in good receivers like the Piksi is slowly drifting into consumer-level hardware. You need to correct for such errors as:
1. Jitter in the code phase vs. phase-locked-loop. As the article describes, most existing codes are long and slow, with bandwidths on the order of 300 m (specifically, 1.023 MHz). The receiver can measure the exact time at which this code changes to get your existing resolution, but the L5/E5 bands are at 20 MHz.
2. Integer offsets when interpreting the carrier frequency. The above slow codes are transmitted on a carrier at 1-2 GHz, giving much higher resolution, but there's no information in the signal as to which particular node of the carrier frequency you're observing. Comparing to a known location, and improving your guess over time, can let you make use of this information.
3. Unknown, slowly drifting ionospheric delay. Typically fixed in industrial or agricultural applications by using a base station and radio link to tell your remote link that the base station (which is bolted to a big chunk of concrete) is now reporting that it's 20 cm from where it was an hour ago, and the remote unit should probably just adjust any measurements by that much.
I only have enough knowledge of the system to be dangerous, but I've wondered whether it would be possible to correct for #3 at a consumer level with a phone app. If you had thousands of phones cooperating in a city, at any given time many would be stationary, even charging or on wifi, and you could theoretically trade off roles as reference base stations and remote receivers. I think it would require a lot more low-level access to the GPS chip than generic Apple/Android phones give you, but it's an idea - feel free to take it and run if you like it.
To answer the basic question - common NMEA protocol returns GPS data with latitude formatted as DDMM.MMMMM (Degrees, minutes, and decimal minutes) and longitude in DDDMM.MMMMM format. Four digits of precision get you a precision of about 1.6 meters, depending on where you are on the Earth, but that doesn't mean you have that level of accuracy.