Editing Projected coordinate system (section)

==Grid reference encodings==
Locations in a projected coordinate system, like any cartesian coordinate system, are measured and reported as easting/northing or (''x'', ''y'') pairs. The pair is usually represented conventionally with easting first, northing second. For example, the peak of [[Mount Assiniboine]] (at {{coord|50|52|10|N|115|39|03|W}} on the [[British Columbia]]/[[Alberta]] border in [[Canada]]) in UTM Zone 11 is at <code>(0594934mE, 5636174mN)</code>, meaning that is almost 600km east of the false origin for Zone 11 (95km east of the true central meridian at 117°W) and 5.6 million meters north of the [[equator]]. 

While such precise numbers are easy to store and calculate in  [[geographic information system|GIS]] and other computer databases, they can be difficult for humans to remember and communicate. Thus, since the mid 20th century, there have been alternative encodings that shorten the numbers or convert the numbers into some form of alphanumeric string.

For example, a '''truncated grid reference''' may be used where the general location is already known to participants and may be assumed.<ref>{{cite web|url=http://www.bivouac.com/PgxPg.asp?PgxId=155 |title=Truncated Grid References |publisher=Bivouac.com – Canadian Mountain Encyclopedia|date=2006-11-17}}</ref> Because the (leading) [[most significant digit]]s specify the part of the world and the (trailing) [[least significant digit]]s provide a precision that is not needed in most circumstances, they may be unnecessary for some uses. This permits users to shorten the example coordinates to <code>949-361</code> by concealing {{code|05nnn34 56nnn74}}, assuming the significant digits (3,4, and 5 in this case) are known to both parties.<ref name=NGA_grids>{{cite web |title=Grids and Reference Systems |url = http://earth-info.nga.mil/GandG/coordsys/grids/referencesys.html |publisher=National Geospatial-Intelligence Agency |access-date=4 March 2014 }}</ref>

Alphanumeric encodings typically use codes to replace the most significant digits by partitioning the world up into large grid squares. For example, in the [[Military Grid Reference System]], the above coordinate is in grid 11U (representing UTM Zone 11 5xxxxxx mN), and grid cell NS within that (representing the second digit 5xxxxxmE x6xxxxxm N), and as many remaining digits as are needed are reported, yielding an MGRS grid reference of 11U NS 949 361 (or 11U NS 9493 3617 or 11U NS 94934 36174). 

[[File:Fictional Map 1.jpg|right|thumb|400px|A typical map with grid lines]]
The [[Ordnance Survey National Grid]] (United Kingdom) and other national grid systems use similar approaches. In [[Ordnance Survey]] maps, each Easting and Northing grid line is given a two-digit code, based on the [[British national grid reference system]] with an origin point just off the southwest coast of the [[United Kingdom]]. The area is divided into 100&nbsp;km squares, each of which is denoted by a two-letter code. Within each 100&nbsp;km square, a numerical grid reference is used. Since the Eastings and Northings are one kilometre apart, a combination of a Northing and an Easting will give a four-digit grid reference describing a one-kilometre square on the ground. The convention is the grid reference numbers call out the lower-left corner of the desired square.  In the example map above, the town Little Plumpton lies in the square 6901, even though the writing which labels the town is in 6802 and 6902, most of the buildings (the orange boxed symbols) are in square 6901.

===Precision===

The more digits added to a grid reference, the more precise the reference becomes. To locate a specific building in Little Plumpton, a further two digits are added to the four-digit reference to create a six-digit reference. The extra two digits describe a position within the 1-kilometre square. Imagine (or draw or superimpose a [[Romer (tool)|Romer]]) a further 10x10 grid within the current grid square. Any of the 100 squares in the superimposed 10×10 grid can be accurately described using a digit from 0 to 9 (with 0 0 being the bottom left square and 9 9 being the top right square).

For the church in Little Plumpton, this gives the digits 6 and 7 (6 on the left to right axis (Eastings) and 7 on the bottom to top axis (Northings). These are added to the four-figure grid reference after the two digits describing the same [[coordinate axis]], and thus our six-figure grid reference for the church becomes 696017. This reference describes a 100-metre by 100-metre square, and not a single point, but this precision is usually sufficient for navigation purposes. The symbols on the map are not precise in any case, for example the church in the example above would be approximately 100x200 metres if the symbol was to scale, so in fact, the middle of the black square represents the map position of the real church, independently of the actual size of the church.

Grid references comprising larger numbers for greater precision could be determined using large-scale maps and an accurate [[Romer (tool)|Romer]]. This might be used in [[surveying]] but is not generally used for land navigating for walkers or cyclists, etc. The growing availability and decreasing cost of handheld [[GPS]] receivers enables determination of accurate grid references without needing a map, but it is important to know how many digits the GPS displays to avoid reading off just the first six digits. A GPS unit commonly gives a ten-digit grid reference, based on two groups of five numbers for the Easting and Northing values. Each successive increase in precision (from 6 digit to 8 digit to 10 digit) pinpoints the location more precisely by a factor of 10. Since, in the UK at least, a 6-figure grid reference identifies a square of 100-metre sides, an 8-figure reference would identify a 10-metre square, and a 10-digit reference a 1-metre square. In order to give a standard 6-figure grid reference from a 10-figure GPS readout, the 4th, 5th, 9th and 10th digits must be omitted, so it is important not to read just the first 6 digits.