The False Precision of Exact Coordinates

A coordinate such as 3.8667421, 11.5173816 looks authoritative.

Seven decimal places suggest that a location has been measured with extraordinary care. Put the point on a map and the software will happily place it at an apparently exact position. Copy it into another system and the digits survive. Export the dataset, publish the map, run a spatial join, calculate distances: at every stage, the coordinate continues to look precise.

Yet the original location might have been recorded from a phone with uncertain positioning, geocoded from an address, estimated from a paper map, copied from another dataset, assigned to the centre of a village, or manually placed by someone who knew only the approximate area.

The digits can be exact even when the geography is not.

That distinction—between coordinate precision and positional accuracy—is easy to lose because computers preserve numbers much more faithfully than they preserve the uncertainty behind them.

Decimal places tell you how finely a coordinate is written

For geographic coordinates in decimal degrees, additional decimal places represent increasingly small angular increments.

Near the equator, one degree of longitude spans roughly 111 kilometres. As an order-of-magnitude illustration, the written resolution therefore decreases approximately like this:

• Decimal places: 0; Approximate longitude increment near the equator: 111 km

• Decimal places: 1; Approximate longitude increment near the equator: 11 km

• Decimal places: 2; Approximate longitude increment near the equator: 1.1 km

• Decimal places: 3; Approximate longitude increment near the equator: 111 m

• Decimal places: 4; Approximate longitude increment near the equator: 11 m

• Decimal places: 5; Approximate longitude increment near the equator: 1.1 m

• Decimal places: 6; Approximate longitude increment near the equator: 11 cm

• Decimal places: 7; Approximate longitude increment near the equator: 1 cm

These values describe numerical resolution, not the accuracy of the location.

The actual ground distance represented by a change in longitude also shrinks towards the poles, while latitude behaves somewhat differently because the Earth is not a perfect sphere. But even if those geometric details were ignored, the larger problem would remain: storing a coordinate to seven decimal places does not establish that anyone ever knew the position to centimetre accuracy.

It only establishes that the number has seven decimal places.

Precision and accuracy answer different questions

Precision is fundamentally about the fineness or repeatability of a measurement or representation. Accuracy concerns how closely the reported position corresponds to the relevant external reference or true position.

In geodetic surveying, NOAA's National Geodetic Survey explicitly distinguishes the two: precision concerns repeatability or internal agreement, while accuracy depends on alignment to an external reference or datum.

The distinction becomes intuitive with a simple example.

Imagine that a device repeatedly estimates the same location as:

3.866742, 11.517382
3.866741, 11.517383
3.866743, 11.517381

Those measurements cluster tightly together. They may therefore be precise relative to one another.

But suppose the true position is twenty metres away because of a systematic error. The measurements remain precise while being inaccurate.

The opposite situation can also occur: several measurements may be relatively scattered, yet their average happens to fall close to the actual position.

Coordinates alone rarely tell you which situation you have.

Software can manufacture precision without manufacturing information

False precision often enters a dataset innocently.

Suppose a coordinate originally recorded as:

3.87, 11.52

is imported into software that stores geographic coordinates using double-precision floating-point numbers. Later, an export writes:

3.87000000, 11.52000000

No new geographic information has been discovered. The representation simply acquired more digits.

A transformation can produce something similar. Reprojecting a location from one coordinate reference system into another involves mathematical calculations that may return many decimal places. Those digits describe the numerical result of the transformation; they do not retroactively improve the accuracy of the original observation.

The distinction between coordinate systems therefore matters here too. Changing how a location is represented can legitimately change its coordinate values without making the underlying location better known.

This becomes particularly important in automated data pipelines. Each stage may preserve or increase numerical detail while the provenance of the original position becomes progressively less visible.

By the time the coordinate reaches a published map, it can look more certain than the evidence that created it.

A point is often a model of a place

There is another source of false exactness that has nothing to do with measurement error.

Not every geographic point is intended to represent an exact physical location.

A point labelled with the name of a town might represent:

• its administrative centre;

• a populated-place centroid;

• the town hall;

• a geocoded address;

• a manually selected representative point;

• the centre of a polygon;

• a location supplied by another database.

All of those can be reasonable representations for particular purposes, but they do not mean the same thing.

Likewise, a point representing a hospital might correspond to the main building, the parcel centroid, an entrance, a mailing address or merely an approximate location identified from available evidence.

Writing the resulting coordinate to six decimal places does not resolve that semantic uncertainty.

The database may know exactly where the point is while remaining uncertain about exactly what that point represents.

That is why geographic accuracy is not purely a matter of measurement technology. It also depends on the relationship between the coordinate and the real-world entity it is supposed to stand for.

Some locations do not have one exact coordinate

The problem becomes even clearer for geographic entities that occupy space.

What is the exact coordinate of Yaoundé?

There is no single natural answer.

A mapping system can return a representative point, administrative centroid, city-centre coordinate or another chosen location, but Yaoundé itself is not a dimensionless point. The same applies to a neighbourhood, forest, lake, market, university campus or protected area.

A point may be useful because a particular task requires one. Search interfaces need places to zoom to. Labels need anchor positions. Tables may require one coordinate pair per record. Routing may need an entrance or access point.

But the point is an operational representation of the place, not the place itself.

This is a broader example of why x-y or latitude-longitude values need context before they become meaningful geography. Even perfectly valid coordinates do not tell you what decision produced them.

Geocoding makes this especially visible

An address can often be converted into coordinates with many decimal places regardless of how the location was inferred.

A geocoder may identify an exact rooftop position. It may interpolate along a street segment. It may return the centre of a postal area, neighbourhood or settlement. It may fall back to a less specific match when the requested address cannot be resolved.

All of these results can be expressed using coordinates of identical numerical precision.

The number of decimal places therefore tells you almost nothing about the geocoding precision or match quality.

A coordinate such as:

4.051056, 9.767869

does not reveal whether the underlying evidence identified a building, a street, a district or merely a city.

The important metadata is not another decimal digit. It is information about how the position was obtained and what level of location it represents.

A future guide on geocoding confidence and match quality can treat that problem operationally. The larger cartographic lesson is that a point can visually suppress the uncertainty of the process that produced it.

Exact-looking points change how readers interpret evidence

A map marker has a strong visual quality: it says here.

That is useful when “here” is genuinely known. It becomes misleading when the evidence really says “somewhere around here”, “associated with this settlement”, or “reported within this area”.

A reader does not normally inspect the coordinate's provenance before interpreting the symbol. A sharply drawn marker can therefore communicate more certainty than the underlying evidence supports.

The cartographic response is not always to make the coordinate less precise.

Sometimes the exact stored coordinate is useful computationally, even when the source is uncertain. Rounding it may throw away information without actually communicating uncertainty any better.

Instead, the representation may need to change.

An uncertain location could be accompanied by a confidence radius, represented as an area instead of a point, grouped at a coarser geographic level, labelled as approximate, or withheld entirely when publishing an exact position would be misleading or unsafe.

The right response depends on what the uncertainty means.

That is part of the broader principle developed in AI Will Not Remove Cartographic Judgement: a technically valid geographic result still requires judgement about what the map should communicate and what its evidence can support. The published essay already argues that the visual confidence of a map can exceed the confidence justified by the underlying evidence.

Rounding is not the same as uncertainty

It is tempting to solve false precision by simply removing decimal places.

Sometimes that is appropriate. A public report may not need centimetre-scale coordinate formatting when the input locations are only known to the nearest hundred metres.

But rounding alone can also be deceptive.

Consider two coordinates both shown to three decimal places. One may come from a high-quality survey that has deliberately been rounded for presentation. The other may be an approximate point estimated visually from a map.

They look equally precise on the page. Their evidential quality is completely different.

Conversely, a high-quality measurement may legitimately retain many digits because those digits are useful for processing even if a map intended for the general public does not need to display them.

The number of decimals is therefore a formatting decision. Uncertainty is a property of the evidence and process.

They are related, but they should not be confused.

Provenance matters more than an impressive coordinate

A trustworthy coordinate should ideally be accompanied by enough context to understand where it came from.

Depending on the use case, that might include:

• the original source;

• the method used to determine the location;

• the coordinate reference system;

• reported positional accuracy or uncertainty;

• whether the point was observed, geocoded, derived or manually placed;

• the date of observation;

• transformations applied after collection;

• the geographic entity the point is intended to represent.

Geospatial standards have long treated positional accuracy and lineage as properties that should be documented rather than inferred from the coordinate string itself. The US Federal Geographic Data Committee's point-data standard, for example, requires spatial-data quality information to address lineage and positional accuracy and notes that positional accuracy should consider the final product after transformations.

This is especially important as data is copied between systems. Coordinates tend to survive transformations and exports very well. Their caveats often do not.

The result is a familiar asymmetry: the location becomes easier to reuse at exactly the same moment that the reason for trusting it becomes harder to recover.

More precision can even create new risks

There are situations where retaining and publishing the most precise available location is not merely unnecessary but undesirable.

Exact coordinates can expose sensitive homes, endangered species, vulnerable infrastructure, field respondents or other locations whose disclosure creates risk.

In those cases, the correct publication decision may deliberately reduce spatial precision through aggregation, generalisation, displacement or access controls.

Again, the important distinction is between the coordinate stored internally and the geographic claim appropriate for the audience.

A system can know a location precisely without being obliged to publish it precisely.

That difference matters because, as A Map Is More Than a Picture argues, a Map carries more than visible geometry: it also has an audience, context and intended way of communicating. The most faithful public representation is not always the one that exposes the maximum amount of underlying detail.

Ask what the digits actually know

Coordinates encourage a peculiar form of trust because they look mathematical.

Names can be ambiguous. Descriptions can be vague. Boundaries can be disputed. But a pair of numbers extending six places after the decimal point feels settled.

That feeling is often undeserved.

A coordinate can be numerically precise because software generated it that way. It can be internally consistent and correctly formatted. It can use the right CRS and appear in exactly the expected location on the map.

And still, the underlying observation may only be approximate.

The important questions are therefore not merely:

How many decimal places does this coordinate have?

or:

Can the GIS plot it?

They are:

How was this location determined? What does the point represent? How accurate is the evidence? And how much certainty should the map communicate?

More digits can describe a location more finely.

They cannot make us know the location better.

References

1. NOAA National Geodetic Survey — Real-Time GNSS Positioning User Guidelines. Distinguishes precision—the repeatability or spread of measurements—from accuracy relative to an external reference.

2. NOAA National Geodetic Survey — Technical Report NOS NGS 67. Discusses why the number of published coordinate digits is a poor substitute for an explicit statement of positional accuracy.

3. Federal Geographic Data Committee — Geospatial Positioning Accuracy Standards, Part 1: Reporting Methodology. Defines a consistent methodology for reporting the positional accuracy of point geospatial data.