By Aileen Buckley, Mapping Center Lead
A representative fraction (RF) is the ratio of distance on the map to distance on the ground. Representative fractions are expressed in the form of 1 followed by a : (colon) and then a number, where the one is the numerator in the fraction, the colon represents the division operation, and the other number is the denominator. Thus, a scale of 1:24,000 can be expressed mathematically as 1/24,000. In fact, on some maps, you will see the RF represented using a division sign.
A representative fraction indicates ratio between the number of units on the map to the number of units on the ground.
Representative fractions are a unit-less relation between one “unit” on the map and how ever many “units” of the same type on the ground. An RF of 1:24,000 means one inch on the map equals 24,000 inches on the ground and one centimeter on the map equals 24,000 centimeters on the ground.
RFs are easy to determine and to insert in ArcMap. To find out the RF of the current map, simply look at the Map Scale drop down on the top bar menu.
The representative fraction for the map is shown along the top bar menu in ArcMap.
To insert an RF on your map, click Insert on the top bar menu, then select Scale Text. The first choice on this dialog, “Absolute Scale”, is a representative fraction (figure 3). As with scale bars, after you select this, you can change many of its properties. Once inserted, you can also double click the RF to change even more properties.
The first option in the Scale Text dialog is used to insert a representative fraction into your map.
Advantages and disadvantages
Representative fractions allow the amount of reduction to be easily understood, but it is harder for most people to determine specific distances on the map because distances must either be multiplied or divided by the RF. Representative fractions are invalid if the map is reduced or enlarged. An advantage of adding RFs to your map is that they are extremely easy to determine in ArcMap – simply look at the Map Scale text on the to bar menu of the ArcMap interface. If you do plan to use an RF and the current scale of your map is a number that is not either standard or rounded off, you should change your map scale before creating the final version of your map so that the RF is an easier number for your map readers to understand. Sometimes it is helpful to provide a scale bar along with the RF to give your map readers the advantages of using both.
A representative fraction can be shown along with a scale bar to help map readers even more.
Design
As with scale bars, this map element should be subtle and it should not draw the attention of the map reader – again, they should have to shift their attention in order to find it on the page. The font size used for the RF should be some of the smallest on the page.
If you use an RF with a scale bar, you should place it directly above or below the scale bar. Which you choose will be determined by the layout of your map, but usually the RF is shown above the scale bar. Oftentimes the text for the RF will use the same font as the text and labels for the scale bar – this keeps both at the same visual plane and it relates them visually for the map reader.
Uses
These scale indicators are often used on smaller scale maps and they will also appear along with other scale indicators (verbal scales or more often scale bars) on larger scale maps. Many maps, including the USGS topographic map series, are primarily known by their representative fraction e.g., 1:24,000 scale quadrangle maps.
Look for a blog entry on verbal scales from me next!
The third most common way to indicate scale on a map is though the use of a verbal scale – these are less common than representative fractions (RFs) but they are usually more intuitive!
About the author
Aileen Buckley
Dr. Aileen Buckley is a cartographer who’s been at Esri since 2003. She finds and shares best practices for mapping and analysis with ArcGIS, which leads her to publish widely and present world-wide.
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FAQs
The representative fraction can be determined by dividing the map distance by the land distance in the same unit. A map's scale is expressed as a numerical fraction that compares linear distances on the map to equivalent real distances on the land, measured in the same units (centimetres, inches, feet).
How useful is the representative fraction? ›
In representative fraction (RF), the scale on the map is expressed in the numerical fraction. Its advantage is that it has universal application. Even people who live in foreign countries can find the distance on the map even if they are not familiar with the units of measurements of that country.
What are representative fractions examples? ›
Representative fractions are a unit-less relation between one “unit” on the map and how ever many “units” of the same type on the ground. An RF of 1:24,000 means one inch on the map equals 24,000 inches on the ground and one centimeter on the map equals 24,000 centimeters on the ground.
What is the representative fraction method? ›
A representative fraction, or RF, shows the relationship between one of any unit on the map and one of the same unit on the ground. RFs may be shown as an actual fraction, for example 1/24,000, but are usually written with a colon, as in 1:24,000.
What is the RF calculation scale? ›
An R.F. scale is a ratio, or fraction, that expresses the mathematical relationship between MAP and LAND. Sometimes the actual dimensions of the object will be adopted on the drawing then in that case it is represented by the scale and RF as Scale: 1 cm = 1 cm or 1 : 1 and by RF = 1 / 1 (equal to one).
How do you find RF in math? ›
The relative frequency is a ratio of the frequency of a data point to the total size of the data set. To calculate it, use the relative frequency formula, and divide the data value's frequency by the total size of the data set. The result will be a decimal between 0 and 1. This is the relative frequency.
What is the biggest advantage of representative fraction? ›
It is represented by a fraction whose numerator is always one. Compared to the Verbal Scale in which one centimeter on the map represents 500m on the ground, the RF is always a better option as the exact distance can be known easily. For a large map, RF can be very much suitable.
How is RF better than the statement of scale? ›
scale is a ratio, or fraction that expresses the mathematical relationship between map and land like 1:24,000 which implies "1 map unit is such as 24,000 land units." As R.F carries no units(inches, centimeters etc) it implies that R.F. scales are compared between different maps. -It has universal application.
How is representative fraction different from scale? ›
Representative fraction: It describes the ratio of the distance on the map to the distance on the ground. Linear or graphical scale: It is a line divided into equal parts along with units, similar to a geometrical ruler.
What is representative fraction in simple words? ›
Answer: The ratio of distance on the map to distance on the ground is known as a representative fraction (RF).
Disadvantages : (i) It is only a fraction in which no system of units is used. Hence, distances cannot be directly measured from it. (ii) Whenever a map is photographically enlarged or reduced, the R.F. will no longer be true. (iii) This is not easily understood by a commonman.
What is representative factor? ›
Explanation: The representative factor is defined as the ratio of the length of the drawing to the actual length of the object. The value of representative factor can give information on whether the scale is enlarging or reducing.
What are the 3 types of scales on a map? ›
Generally, scale is a form of size. Map or cartographic scale is the ratio of a distance on Earth compared to the same distance on a map. There are three types of scales commonly used on maps: written or verbal scale, a graphic scale, or a fractional scale.
What is a representative fraction on a fractional map scale? ›
A map scale might be given in a drawing (a graphic scale), but it usually is given as a fraction or a ratio-1/10,000 or 1:10,000. These "representative fraction" scales mean that one unit of measurement on the map 1 inch or 1 centimeter represents 10,000 of the same units on the ground.
What is fractional scale? ›
Ratio or Fractional Scale: the ratio between a distance on a map and the actual distance on the ground – 1:62,500 (or 1/62,500) means that one unit (e.g., an inch) on the map equals 62,500 of the same units on the ground.
What is the representative fraction 1 50000? ›
1: 50,000 means that. 1 unit of the map represents 50,000 units on the ground. or 1 cm represents 50,000 cm. or 15 cm represents 50,000 × 15/100,000 km.
What is a representative fraction on a linear scale? ›
Representative fraction: It describes the ratio of the distance on the map to the distance on the ground. Linear or graphical scale: It is a line divided into equal parts along with units, similar to a geometrical ruler.
