# Decimal Degrees – Understanding Precision Versus Accuracy

## Defining Precision and Accuracy

Precision refers to the level of measurement and exactness of a value. It relates to the fineness of an operation or the degree to which repeated measurements show the same results. Accuracy refers to how close a measured value is to the true value. An example to illustrate the difference is shooting arrows at a target. If all the arrows consistently hit close together in a tight cluster, they have high precision. However, if the cluster of arrows is slightly off the bullseye, then the shots have high precision but low accuracy. The images below demonstrate this visually.

In the context of geographic coordinates and decimal degrees, precision refers to the number of decimal places used. More decimal places allow locations to be specified in finer detail, so it increases precision. However, those decimal places may not actually reflect the true location accurately. Accuracy depends on how precisely the location was measured and is typically limited to a certain number of decimal places due to measurement limitations.

### Common Misconceptions

A common misconception is that more decimal places inherently means more accuracy. But high precision only leads to high accuracy if the measurement methodology supports it. Extending a latitude coordinate to 8 or 10 decimal places does not make it more accurate if the equipment is only accurate to 4 decimal places.

## Why Precision Matters in GIS

### Inaccurate Coordinates Lead to Wrong Locations

Insufficient precision in recording geographic coordinates can lead to imprecise location values that fail to pinpoint the intended location correctly. For example, a study plots tree sampling locations using GPS receivers that record geographic coordinates to 3 decimal places. But truncating or rounding the coordinates to that level of precision places the samples on the wrong sides of property lines, roads, streams, and other important landscape features. Thus lack of precision directly causes real-world inaccuracies.

### Precision Allows Pinpointing Locations and Analysis

Higher precision allows geographic data locations and relationships to be represented at finer resolutions. For example, epidemiological analysis aiming to correlate health patterns with proximities to specific pollution sites depends on location values precise enough to capture meaningful distance gradations. And transportation planning looking at intersections and bridges requires sub-meter precision to represent infrastructure elements correctly.

So for many GIS analyses, precision enables capturing geographic realities better than coarse coordinates could. Those seeking to understand landscape factors in species habitats, connect economic characteristics to neighborhoods, or model environmental processes require location precision aligned to their application requirements.

## Improving Precision in Decimal Degrees

### Increasing Number of Decimal Places Improves Precision

A straightforward way to improve geographic coordinate precision is increasing the number of decimal places when capturing and recording location values. Commercial GPS units typically provide readings to 5 or 6 decimal places but may accept inputs for specifying up to 9 places. GIS databases can store values up to double precision with very fine units in the 15th or 16th decimal place. So supporting infrastructure allows pushing precision quite far in principle.

Best practice is to record coordinates at the highest precision supported by the measurement approach and use case accuracy needs. With satellite imagery reaching sub-meter resolution, climate phenomena trending on micro-regional levels, and facilities data guiding emergency response, precision translates to real-world performance.

### Best Practices for Recording Decimal Degrees

To optimize precision in practice, adhere to several key guidelines:

- Be consistent in precision across datasets for analysis
- Record more precision than needed then round/truncate later if required
- Include precision metadata in supplemental attributes
- Use all decimal places provided by measurement devices
- Encode values using 64-bit double precision if software allows

Precision should match analysis use cases but excess decimal places causing false precision should be avoided.

### When to Round Versus Truncate Geographic Coordinates

Rounding and truncating handle excess decimal places in different ways. Rounding looks at the digit in the next decimal place, with values above 5 rounding up and below 5 rounding down. Truncating simply removes the extra decimals without consideration of rounding math.

Best practice is to truncate rather than round geographic coordinates if reducing precision. This avoids inadvertently moving location values when that is not intended. Some judgment does come into play, such as handling recurring 9s that could stem from conversion or input limitations.

In any case metadata should state the original and modified precision for clarity.

## Balancing Precision and Accuracy

### Accuracy Places Limits on Meaningful Precision

Despite the benefits of high precision, accuracy fundamentally constrains how many decimal places have legitimacy. Extending decimals beyond measurement accuracies misleadingly implies greater accuracy than the equipment or methods can support. So a realistic balance should account for these factors.

For example, consumer grade GPS units provide readings typically accurate to 14-16 feet under good conditions. This corresponds to about 5 decimal places for latitude and longitude coordinates. Extending coordinates to 8 decimals then lacks meaning regardless of software or database storage precisions.

### Guidance on Appropriate Precision for Different Uses

As a rule of thumb, the table below provides guidance on relating coordinate precision needs to common use cases:

Use Case | Minimum Precision |
---|---|

General region identification | 2 decimal places |

City-scale localization | 3 decimal places |

Neighborhood analysis | 5 decimal places |

Property delineation | 6 decimal places |

Land surveys | 8 decimal places |

Scientific micro-studies | 10+ decimal places |

Matching coordinate precision to analysis and application needs ensures meaningful location specificity without false precision.

### Code Examples Showing Precision versus Accuracy Tradeoffs

Looking at code usage provides further insight into managing precision versus accuracy. The examples below demonstrate PHP and JavaScript code handling coordinates at different precisions and rounding or truncating values.

#### PHP Decimal Precision Handling

“`php

// Store coordinate with maximum precision

$lat = 41.6534291655839;

// Round to 5 decimals for accuracy

$displayLat = round($lat, 5);

// Truncate to 4 decimals

$storeLat = substr($lat, 0, 9);

“`

#### JavaScript Coordinate Rounding

“`js

// Receive coordinate from input

let coord = 41.768637936;

// Round to 5 places for display

let displayCoord = coord.toFixed(5);

// Truncate to 4 places for storing

let storeCoord = Math.trunc(coord*10000) / 10000;

“`

The examples demonstrate balancing storage versus display precisions and when to round versus truncate based on use case.

## Checking and Communicating Precision

### Techniques for Validating Precision and Accuracy

Verifying precision and accuracy helps identify any mismatches requiring correction. Some approaches include:

- Checking values against known accurate baseline coordinates
- Comparing datasets with overlays and location-specific testing
- Looking at clustering and statistical distributions
- Spot validation with higher precision measurement methods

Automated geoprocessing scripts can also run validation operations documenting precision issues. Ideally discrepancies trigger updates from re-collection or verification if the more precise values reflect truth more accurately.

### Metadata Standards for Documenting Precision

Spatial data metadata provides the critical information needed to understand coordinate precisions and accuracies. Standards facilitate consistent metadata contents across organizations and GIS platforms. The main metadata specifications related to precision include:

**FGDC:**Horizontal/Vertical Positional Accuracy elements**ISO 19115:**DQ_AbsoluteExternalPositionalAccuracy metrics

Following recognized metadata standards ensures precision transparency needed for proper analysis and handling.

### Conveying Precision Appropriately to Users

How precision gets communicated to end-users plays a key role in appropriate coordinate usage. Map displays may adaptively round coordinates based on zoom levels while still storing full precision in the background. Or precision readouts may indicate differential GPS versus consumer grade coordinates. Conveying context alongside raw coordinate values encourages matching precision realistically to user needs.