copyright 2023 daniel kalak
licensed under cc by nd 4.0

geocoordinates tell you how far north or
south of the equator and how far east or
west of an arbitrary meridian you are. the
standard meridian today goes through
greenwich in london. but other candidates
have also been used. one goes through
paris. another lies just west of the
island of ferro, the western end of the
known world at the time. but the ferro
meridian runs right through iceland, so
depending on your definition, it might not
even lie west of all of europe.

let us assume that the earth is a perfect
sphere, and that the distance from the
north pole to the equator is exactly
10,000 kilometers. that was the original
definition of the meter by the french.

let us divide a full circumference into
360 degress, every degree into 60 minutes,
and every minute into 60 seconds.

then changing a set of geocoordinates by
... will change the position by no more
than about

1 degree ...  111 kilometers
1 minute ... 1852 meters
1 second ...   31 meters

the numbers are rounded to the closest
integer. today, a nautical mile is defined
as exactly 1852 meters. keep in mind that
moving east or west by 1 degree or minute
or second changes your position by fewer
and fewer meters the closer you get to the
poles.

let us continue to use degrees, but use
decimal places of a degree instead of
minutes and seconds.

then changing the last digit by a single
step will change the position by no more
than about

0 decimal places ... 111 kilometers
1 decimal place  ...  11 kilometers
2 decimal places ...   1 kilometer
3 decimal places ... 111 meters
4 decimal places ...  11 meters
5 decimal places ...   1 meter

the numbers are rounded to closest
integer. dividing a full circumference
into 400 gradians, also known as gons,
instead of 360 degrees, would have made
the numbers prettier.

so you probably dont need as many decimal
places on your coordinates as you might
think. see also xkcd 2170.

and making sure that a set of coordinates
points to an exact location on the earth,
which is neither a perfect sphere nor a
perfect ellipsoid, is a whole different
story anyway.