• GEOGRAPHIC COORDINATE SYSTEMS •
For convenience, we sometimes treat the earth as though it was 2 dimensional. Think paper maps and computer screens. But there's no getting around the fact that the "real" earth is a 3dimensional solid and defining locations on it's surface starts with choosing one or another of the mathematical models that the science of geodesy (earth measurement) has come up with over the years. These earth models, more properly called "datums", address the physical properties of the earth such as size, shape and axis of rotation. They also capture arbitrary properties such as the location of the prime meridian. Geographic coordinate systems express locations as angles of latitude (northsouth) and longitude (eastwest). The Latitude and Longitude article on the National Atlas website explains it very well.
GCS Coordinates Come In Three Flavors 

Northern Hemisphere Latitudes Eastern Hemisphere Longitudes 
Southern Hemisphere Latitudes Western Hemisphere Longitudes 

GCS Coordinates Are Numbers
Numbers^{ }used to define location are scientific measurements in the same sense as any measured variable.
The rules governing the accuracy and precision of numeric information apply.
Regardless of the mathematical model used (DMS vs DM vs DD), the number of decimal places (precision) in a GCS
coordinate pair should reflect the accuracy of the method used to determine the values.
Accuracy  DMS  DM  DD  Acceptable Accuracy and Precision For 

+ .0001 meters  ddd mm ss.ssssss  ddd.dddddddddd  Some survey control  
+ .001 meters  ddd mm ss.sssss  ddd.ddddddddd  Some survey control  
+ .01 meters  ddd mm ss.ssss  ddd.dddddddd  Cadastral mapping  
+ .1 meters  ddd mm ss.sss  ddd.ddddddd  Cadastral mapping  
+ 1 meter  ddd mm ss.ss  ddd.dddddd  Some natural resources mapping  
+ 10 meters  ddd mm ss.s  ddd mm.mmm  ddd.ddddd  Most natural resources mapping 
+ 100 meters  ddd mm ss  ddd mm.mm  ddd.dddd  Some natural resources mapping 
+ 1000 meters  ddd mm.m  ddd.ddd  Rougher mapping  
+ 10,000 meters  ddd mm  ddd.dd  Really rough mapping 
See our Lambeau Field example for another way to look at coordinate pair precision
GCS Coordinates Are Not Just Numbers
A^{ }GCS coordinate pair used in written or spoken communication should correspond to one,
and only one, point on the earth's surface.
That means there's more to it than getting the numbers right:
 The name of the Geographic Coordinate System (and the associated datum) must be stated  there is no standard
 The pair order must be stated  there is no standard for which comes first, latitude or longitude
 DMS and DM coordinate pairs must include units so that degree, minute and second values can be distinguished from oneanother
 Latitude values must specify northern vs southern hemisphere to make sure points wind up on the correct side of the equator
 Longitude values must specify eastern vs western hemisphere to make sure points wind up on the correct side of the prime meridian
 DD coordinate pairs should be structured for recognition by computer software (no nonnumeric characters)
A simple table is an efficient way to insert GCS coordinates in to written work:

An algebraic expression is another way to do the same job:
WGS 84 lon/lat = 87° 54' 58.9" W / 44° 31' 40.2" N 
GCS  OMG !!
Sometimes^{ }folks use geographic coordinates in their work without fully understanding the mathematics and symantics.
Work products can get released into the wild containing undefinitive coordinate pairs
(don't correspond to any real place) and ambiguous coordinate pairs (correspond to more than one real place).
The usual result of these miscues is minor embarrassment, but sometimes the consequences are more serious.
Official records of important land features or events can wind up incorrect or incomplete.
We've collected some "howto" and "hownotto"
examples.
GCS Coordinates and Distance Measurements
Geographic^{ }coordinates are great for expressing location, but they are lousy for expressing distances.
Here are some rules of thumb that can help when you have to jump back and forth between linear and angular distances.
 Earth circumference (360°) ~ 40,000 kilometers
 1^{ }degree of latitude ~ 111 kilometers (69 mi)
 7½ minutes^{ }of latitude ~ 14 kilometers (8.6 mi)  this number is significant because the map tiling scheme for USGS topo maps is based on 7½ minute quadrangles.
 1^{ }minute of latitude ~ 1850 meters (1.15 mi)
 1^{ }second of latitude ~ 31 meters (102 ft)
 .00001^{ }degrees of latitude ~ 1.11 meters (3ft 8in)  this number is significant because most natural resources work uses coordinates computed to five decimal places.