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A. Map Scale

B. Measure up Scales

C. Accuracy, Precision, and far-reaching Digits

D. Classification, Simplification and Symbolization of Data

A. Map range

Map scale is the relationship between a unit of length on a map and also the equivalent length on the ground. We will use ideas of map scale throughout the course, for this reason it will pay girlfriend to study this ar carefully.

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1. Varieties of Map Scales

We deserve to relate map and also ground with three different types of scale. Verbal scale expresses in indigenous a relationship between a map distance and a soil distance. Generally it is along the lines of:


One customs represents 16 miles.


Here that is implied that the one inch is top top the map, and also that one inch represents 16 miles on the ground. Verbal scales are typically found on renowned atlases and maps.

The second type of scale is a graphic scale, or bar scale. This shows straight on the map the corresponding ground distance. Because that example:




The third kind of range is a representative fraction, or proportion scale. Compared to the first two, it is the many abstract, but additionally the most versatile. A representative fraction, or RF, reflects the relationship between one of any kind of unit on the map and also one the the very same unit on the ground. RFs might be presented as an really fraction, for example 1/24,000, yet are usually written v a colon, as in 1:24,000. In this example, one unit of any length (one mm, one cm, one inch, one foot, etc.) ~ above the map to represent 24,000 of those exact same units on the ground (24,000 mm, 24,000 cm, 24,000", 24,000", etc.). The RF is versatile since you are not tied come any details units. You might work in any unit friend choose, either metric, English, or other.

The RF is a referred to as a fraction because the is just that--a portion that shows just how much the real civilization is diminished to right on the map. A good comparison is frequently made with range models the automobiles or aircraft. A 1/32-model of an auto is 1/32nd as big as the actual auto. In the very same way, a 1:100,000-scale map is 1/100,000th as big as the floor area shown on the map.

A related idea is that of little scale versus big scale. Geographers usage these terms in different way than many people. A big scale map is wherein the RF is reasonably large. A 1:1200 map is therefore larger scale than a 1:1,000,000 map. The 1:1,000,000 map would normally be dubbed a small scale map. This is true even though the 1:1,000,000 map would show a much bigger area than the 1:1200 map.

Here is a dominance of ignorance for dimension of range by RF:



Size the ScaleRepresentative Franction (RF)
Large Scale1:25,000 or larger
Medium Scale1:1,000,000 come 1:25,000
Small Scale1:1,000,000 or smaller


Of course, what is little or big scale is relative. I noticed a surveying text (Brinker & Wolf, 1984) the classed anything smaller than 1:12,000 as small scale -- surveyors rarely job-related with anything smaller sized than this.

The large/small range terminology can come to be confusing as soon as talking about large versus little areas. If you are talking about a phenomenon the occurs across a huge region, the is tempting come say it"s a large-scale phenomenon (e.g., "the woodland blight is a massive disease"). But due to the fact that the map that would show this would certainly be small-scale, that is better to use a different term to stop confusion. My favourite is "broad-scale."

Many maps include two or also all three species of scales. USGS topographic maps have both bar scales and RFs.

2. Converting between Scale Types

If girlfriend are offered one type of scale, friend should be able to derive or construct any kind of of the other two. This takes some practice, and some troubles are consisted of in her lab exercises. Some instances are offered below.

A an important step in doing any kind of kind of conversion that requires differing units is to incorporate the systems in the trouble itself. You can then publication the devices by multiply or dividing. This way you avoid ending up being confused about which conversion factors to use and also how to usage them.

Verbal range to RF

The crucial here is to write the verbal scale as a fraction, then transform so the both numerator and denominator have actually the very same units, and the numerator has a 1.


(a) convert verbal range of "1" come 18 miles" to RF





or 1:1,140,000.

Notice that the resulting portion is rounded so the the RF does not imply an ext accuracy 보다 the original precision warranted.


(b) transform verbal range of "15 cm to 1 km" to RF




or 1:6700.

In countless conversions you have the right to save procedures if friend remember extr equivalencies.

For example, in (a) above, we might have provided the fact that 1 mile = 63,360 inches to skip a step.

Verbal scale to graphic Scale

Usually this is a relatively easy task if the map offers us reasonable devices in the verbal scale. We have the right to use the linguistic scale like a fraction to change the ground street to map distance.


(c) transform verbal scale of "1 centimeter to 14 km" to a graphics scale.


One centimeter is a reasonably small distance, so we probably don"t desire our bar scale to have major divisions lot smaller than this. A centimeter represents 14 km, therefore a department of 10 kilometres is most likely fine. Thus we want to find how countless centimeters represent 10 km.




In other words, we can represent our 10 km increment top top the bar scale by measuring turn off 0.71 cm on the map. We"d draw the an initial tick at 0.71 cm, the second at 1.42 cm, and also so on:




RF to Graphic Scale

This to add an extra step to the instance above. Us can uncover the map-distance identical of a soil distance, however we likewise need to be careful around choosing i m sorry ground distance we want to portray top top the map. Probably it"s most basic to pick a smaller ground distance that you can then multiply to get a reasonable bar scale.


(d) transform an RF that 1:250,000 to a graphic scale


If we aren"t certain what increments a bar scale would have actually for this scale, we could start out, say, v finding the map indistinguishable of 1 mile:



This might work fine, v one mile significant off ~ above the map every 0.25 inch; or, we may want finer or more comprehensive increments, which we can discover by dividing or multiplying the .25" together needed.

RF to verbal Scale

Again we need to choose appropriate units to convert into. Most verbal scales room either "one inch represents ____ miles," or "one centimeter represents ___ kilometers." this are fairly easy come do, due to the fact that it means only the we convert the denominator of ours RF to the bigger units.


(e) convert from RF that 1:25,000 to a verbal scale, in metric



1 centimeter ~ above this map represents 1/4 of a kilometer on the ground.

Graphic scale to RF

Here we need to take a measurement from the bar range to determine the map street that synchronizes to a floor distance.


(f) uncover the RF scale for the adhering to graphic scale



By measuring v a ruler, we discover that 10 kilometers steps 2.4 cm. We can use this connection to discover the RF because that the bar scale:




3. Determining scale from a Map or Photo

Some maps might come with no scale at all. Aerial photographs practically never do (unless one to be painted top top the ground prior to the photograph was taken!). How can you have a scale for use v the map or photo?

Actually the procedure is very similar to the last example above. But instead of measuring follow me a bar scale, you have to measure the size of an object on the map or photograph whose actual size you know. This might be a football field, a city block, or the Equator (if it"s a people map). Frequently you have the right to identify 1-mile-square part in the us (see the account below, under survey Systems). Girlfriend may also need to go out to the location mapped or pictured and measure the distance between two i can identify objects.

Once you have actually the 2 distances, friend can find the range as above. For an additional example, suppose you have a map whereby the distance between two section-line roads is 3.5 customs on the map. We can usually assume this is one mile top top the floor (there room exceptions). The RF scale is then:




One caveat (exception) because that air photos is the this technique assumes the two areas are in ~ the very same elevation--or that the terrain is flat. If you space using air photos, the terrain may not be flat. If there are hills, also moderate ones, the calculations can be thrown off. Store this in mind for later on in the course.

Another method to calculate range on one unknown map or picture is to compare it come a map v a well-known scale. Because that example, expect you have actually an air picture where the distance between two hills is 7.2 centimeters.You have actually a map of the same area in ~ 1:24,000, and on the map the distance in between the hills is 2.4 centimeters.

The answer involves a tiny algebra. Because the ground distance is the exact same on both photo and also map, we can produce an expression for this ground street for both, and also then put them top top either side of an equation. The ground distance have the right to be uncovered by multiply the map/photo street by the scale (in this case, through the train station of the scale--notice just how this provides the devices cancel correctly). We must find, for the photo, how countless ground systems are stood for by one unit top top the photo, so we usage an x because that this unknown quantity and solve because that it:








we can cancel the systems on every side and also divide through 7.2:






In other words, the RF scale for the picture is 1:8,000.


4. Identify Distance and Area indigenous Map & Scale

Map range isn"t much use in and of itself. We have the right to use a map"s range to recognize distances and areas on the map. Contrasted to converting in between scale types, calculating distance is simple. Area calculations space trickier, since we need to square the numbers.

Finding distance from map and also scale

As an example, mean we have actually a map through a scale of 1:50,000. We measure the distance follow me a residential property boundary as 1.7 cm. What is the size in the genuine world?




To find ground distance, we have to use the map scale to transform map street to soil distance. Notification that again we inverted the RF scale, for this reason the systems will release properly. As soon as we multiply by the scale, we require to transform the ground street to units suitable for ground measurement--in this case, native centimeters to kilometers.

We can likewise calculate distance from verbal and graphic scales. V verbal scales, we usage the same procedure as above with the RF. The only difference is that we have to use the units given in the verbal range (e.g., 1 inch to 17 miles). We"d probably want to measure our map distance in the exact same units (in this case, inches) to do our conversion easy.

Graphic scale are most likely the scales most generally used through laypersons. You have the right to mark off a street on the map and compare it straight to the bar scale. You require not know how plenty of inches or centimeters the map street is. The key drawback that bar scale is the they space usually brief compared come the map itself, and hence measure longer ranges is difficult.

Finding area measurement indigenous map and scale

Area need to be to express in areal units, which room usually distance devices squared -- cm2 , mi2, and so on. Us must as such used squared conversion components when recognize area native map measurements.

For example, expect we measure a rectangular piece of residential property that is 3 cm by 4 cm on a map. The map is in ~ a scale of 1:24,000. What is the area that the parcel?

The area that the package on the map is










on the ground.

Since this is a huge number, we can want to interpret to various other units. There are 10,000 square meters per hectare, therefore the area is 69 hectares (ha) (a hectare is about 2.5 acres). Or, there space (1,000)2 = 1,000,000 square meters per square kilometer, for this reason the area is likewise 0.69 km2.

Notice that by writing the devices as part of the problem, and squaring them along with the numbers, our systems cancel properly and also we end up v a judicious answer.

There is another method to tackle area troubles if you have distance dimensions prefer 3 x 4 cm to begin out the problem. You can transform the distance dimensions come real-world distances first, and also then main point them to uncover the area. This makes the problem longer however perhaps simpler.

B. Measurement scales

1. Definition

Any type of information on a map (or in a table, a list, a survey, etc.) have the right to be defined in state of how pieces of the information can be regarded each other. Examples of mapped information include land-use classes, roadway classes, city populations, and also county areas.

We can think the these varieties of details as either categorical (or qualitative) or numerical (or quantitative). Categorical information can only be explained qualitatively, whereas item of number information can be contrasted quantitatively. That is, numerical info is ~ above a actual scale, together as street (e.g., kilometers), area (e.g., hectares), or temperature (e.g., Celsius).

Example of categorical information:Land-Use category of :1= forest, 2 = grassland, 3 = urban;We can not say that based on the classes, 1 + 2 = 3 !We can only use the number is numbered to describe the items qualitatively.Example of numerical information, city populations:Springfield = 100, Harmony = 200, Centerville = 300;We can say that Centerville has as many people as Springfield and Harmony.

2. 4 Measurement Levels

The categorical and also numerical types have traditionally to be further broken down, each right into two levels of measurement:

Categorical information deserve to either it is in nominal level or ordinal level . In ~ the nominal level, categories simply define different varieties of things, and cannot be compared to each other. Ordinal-level category can, on the various other hand, be ranked against each other.

An example of ordinal level would be roadway classes the interstate, primary, secondary, and primitive; back two primary roads don"t make an interstate, you can say in a sense that interstates space at a greater level than the others, at least in state of price to build!

The land-use classes would certainly be an example of nominal-level measurement. You probably wouldn"t location the classes versus each various other (unless you favor one over the other, in which situation they could be ordinal!).

Numerical information have the right to either be interval level or ratio level . This difference is subtle, and also borders on artificial. The only distinction is the ratio-level info is top top a range that has a true zero, the is, a zero the truly represents a lack of whatever it is you"re measuring.

One that the few common examples of an interval range is temperature. You can compare 2 temperature readings quantitatively. For example, 20 C is 15 levels warmer than 5 C. But the Celsius scale has actually an arbitrary zero allude (the freeze temperature that water, or 32 F). 0 C doesn"t mean a lack of temperature. For this reason, 20 C is not four times as heat as 5 C! (One temperature scale, Kelvin, does feature a true zero -- 0 K is -273 C, the temperature in ~ which every molecular movement ceases). Fortunately, over there are few examples that this on maps. You might want to include an exception for elevation, which have the right to be listed below sea level, or longitude, where the 0° heat (Prime Meridian) is arbitrarily attracted on the globe.



Table 2: measure Levels




Measurement Level





Simple categories; cannot rank categories

Colors; land usage types; computer components



Distinct categories; canrank categores in order

Road classes; odor preferences



Continuous scale; measure with numbers; realzero

Temperature; longitude, compass direction



Continuous scale; measurewith numbers; actual zero

Distance; weight; bank balance

Most numerical scales room ratio-level. We deserve to compare 20 kilometres with 10 km in any variety of ways, including saying the first is twice as far as the second.

3. So What?

We will usage this terminology frequently to describe the kinds of information on maps and also in various other sources. Girlfriend will additionally encounter that elsewhere, i guarantee it!

Information regularly is analyzed from one level to another. The general rule is the it"s much easier to translate to a reduced level (e.g., from proportion to ordinal) than to a higher level. In most cases, it"s impossible to walk legitimately come a greater level. Why bother using a lower-level scale? frequently it saves space and energy to use a reduced scale.

For example, if you have actually a table the city populaces in Sonoma ar (i.e., ratio level) and want to show populace on a map, you might print a number beside each city name. This would keep your ratio-level data top top the map itself. A more common method is to have a set of increasingly huge symbols because that the city location, each symbol describe a range of population. These icons would offer ordinal-level information around population. This conveniently reduces the clutter top top the map, however you cannot recuperate the initial ratio-level number from the map.

C. Accuracy, Precision, and far-reaching Digits

1. Accuracy versus Precision

Some human being make a distinction between accuracy and also precision.

Accuracy would certainly be exactly how close a measured worth is come the actual value.

Precision would certainly be the variety of digits reported v the value. Because that example, I added a thermometer come my vehicle that shows the outside temperature to one per 10 of a level (e.g., 65.2° F). The thermometer"s precision is to one per 10 of a level Fahrenheit. But it often seems to give readings that room too high, perhaps as result of the engine"s heat nearby. That accuracy, then, might only be to within 5° F.

2. Significant Digits

Significant digits space the number of digits in a worth that have actually real definition and reflect the accuracy that the value or measurement. Because that example, a distance measurement that 45.8 kilometres would have actually three far-reaching digits. The value means that the measurement was made come an accuracy of tenths of a kilometer. If the instrument, such as an odometer, is no accurate, the value need to not include as many far-reaching digits. The course, if the instrument measures an ext accurately 보다 this, the value need to be reported v the suitable precision.

The main allude is come beware measurements with highly precise values as soon as the accuracy might be referred to as into question. This is specifically true when converting worths from one kind of scale to another. For example, if ns measure a map distance as 11 inches through an simple ruler, then desire to convert to centimeters, I discover on mine calculator:


(11 in.) * (2.54 cm/in.) = 27.94 cm


But 27.94 cm indicates high accuracy, which i didn"t have actually with the original measurement. The solution below is to ring the answer to about the same number of far-ranging digits together the original measurement. In this case, i should most likely say the street is 28 cm.

More example of far-ranging digits:

Two significant digits: 3700, 37, 3.7, 0.37, 0.0037Four significant digits: 19120, 19.12, 0.001912, 19.00, 0.1900

Notice the zeroes included after the decimal point imply precision same to any type of other digits. Normally, zeroes to the appropriate of various other digits (e.g., 3700) room not thought about significant, uneven a decimal suggest is included and much more zeroes happen to the right of it (e.g., 3700.0 implies 5 far-ranging digits). What if we have a measurement of 1900 where the zeroes room significant? Traditionally, a bar is put over the zeroes to suggest significance.

Another equipment is to use clinical notation.

For example, 3700 through the zeroes actually being far-ranging can be created as 3.700 x 103. This breaks the number down right into the mantissa (the far-reaching digits, below 3.700) and the exponent ~ above the ten (here 3). In clinical notation, only one number is placed before the decimal allude in the mantissa. The exponent on the 10 shows how numerous places the decimal point should be relocated to restore the number to simple notation (in this case, three places to the right; this is identical to multiplying the mantissa by 1000). Negative exponents mean smaller numbers, and we transition the decimal point to the left. For example, 3.700 x 10-4 is the exact same as 0.0003700. Clinical notation is handy through very huge or tiny numbers. Number in clinical notation can be used just like other numbers, as long as you follow the rules of exponents -- because that multiplying, dividing, etc.

D. Classification, Simplification and also Symbolization that Data

This is no a food in cartography, for this reason we will certainly not deal in information with how data is classified and also simplified for mapping, and how symbols are developed to fit those data. Yet you have to be aware that any map, consisting of topographic maps, is the an outcome of a the majority of processing the the data behind the map. Here is a brief discussion the some elements that enter data handling for maps.

1. Classification

Maps must take the relevant data and also assign it come a given variety of classes, each through its own number of members. Instances are maps of land uses and also of temperature. For categorical data like land uses, the is simple to overload the map reader through too countless classes. Cartographers introduce a maximum of five or six different classes (for floor use, these can be forest, rangeland, cropland, water, and urban). Number data shown on isarithmic maps (which present zones of equal values) deserve to be somewhat more complex. For example, temperature zones have the right to trend from 80"s F to -20"s F. However the data must be shown with reasonable symbolization (see below).

Data deserve to be damaged down right into categories in three ways:

(a) Each classification can have an equal variety of members. Because that example, in a map the US population by state, we can have 5 categories of population, each through ten states.

(b) Each category could expectations an equal interval of values. In the population map, we would certainly take the range of populations (highest state minus lowest state), and also divide the range by five. Each group would be one-fifth the the as whole range. In this map, categories might have various numbers that states. The highest classification may only have actually a couple of states (e.g., California, new York and also Texas), and also other category may have actually a huge number the states.

(c) Finally, we might subjectively assign claims to classes, probably by in search of "natural breaks" in populace rankings. Regularly map-makers start out with among the very first two methods, climate refine the by looking in ~ the results and an altering classes slightly. Every one of this must reflect the functions of the map. Various methods can develop radically different-looking maps (see any cartography message for examples).

2. Simplification

A second major task in map-making is simplifying the information behind the map. Category is one method of simplifying the data we usage going right into the map. Often this requires lowering the measurement level of the data (such together transforming ratio-level data come ordinal-level data, together in our instance of city populations shown by various circle sizes).

Another simplification job relates come the spatial elements of the data. For example, such as mountain roads might take countless twists and turns. A map that reflects all these curves would certainly be cluttered and also messy. We might want to generalize the road spatially come clarify things. Beware, of course, those map customers who curse you for those curve they didn"t expect! The cartographer"s project is to leveling without distorting and misleading the map user.

Sometimes the task might necessitate eliminating features altogether. For example, a small-scale united state map can display only selected cities; how do you choose which urban to encompass without offending too countless people? I experienced a united state map newly that consisted of moderate-sized cities but omitted mine hometown, mountain Diego (now the 6th largest city in the US).

3. Symbolization

Symbolization of information is another an important part of communicating through maps. What signs are liked will affect whether will world will understand, or also use, a map. Symbols need to be preferred so that the intended audience will understand them. Various symbols need to be supplied for general-purpose maps 보다 those intended for specialists in a field.

Symbols have the right to be inserted on a continuum in between intuitive and abstract. Intuitive symbols indicate to the leader what they represent. Pictographs are recognizable representations of the really objects. Because that example, marshes space often displayed with swampy grass symbols, or airports as planes. Top top the other excessive are abstract icons with no noticeable connection come what castle represent. Instances are circles together cities, or streams together dotted lines. Some abstract symbols have been used so widely to represent a specific feature that, although abstract, castle do attach with the thing in most people"s minds. A star in ~ a circle, because that instance, usually method a funding city.

Symbols can likewise be classed according to their dimension: suggest (0-dimension), line (1-dimension) or area (2-dimension) symbols. Favor the other two, point symbols can convey categorical or number information. Instances of categorical allude symbols are airports, campgrounds, springs, and quarries. Variable-sized circles because that city populace would be examples of numerical suggest symbols.




Line symbols have the right to convey information around linear features, such together roads, railroads, and also streams. One more important use of currently on maps space isolines. Isolines (also called isarithms) connect points of equal value. You"ll often see these on a map of temperature on the weather web page of the newspaper. Every ar along one isoline on this map has actually the very same temperature, at the very least theoretically. This implies likewise that places between two isolines have actually values somewhere in between the worths of the neighboring lines. Without additional information, us cannot say through confidence much more about intervening values. We deserve to estimate, or interpolate, the intervening values, for example by measure up the street of a suggest from every line. Over there is no guarantee, the course, that our estimate is really correct, therefore beware such approximates from isoline maps.




An important kind of isoline because that this food is the elevation edge . These isolines present equal elevations, and are contained on all USGS topographic maps. The edge interval is the elevation difference in between each contour. Contour intervals top top USGS maps vary relying on the terrain. Typical intervals ~ above 1:24,000-scale maps space 20, 40 and 80 feet. A 20-foot interval would certainly show, because that example, contours at 0 (sea level), 20, 40, 60, 80, and so on.

It take away some exercise to feel comfortable working v elevation contours and also other isoline maps. We will have lab practice to give you some exercise with them, including visualizing terrain and also constructing profiles, or two-dimensional views of how elevation changes on a line across the topographic map.

The zones between isolines are regularly shaded or colored to portray the information more effectively. Temperature maps in most newspapers are now in color, with warmer zones acquiring "warmer" colors, colder locations "cooler" colors. These shaded-isoline zones space a blend of line and also area symbols.

Speaking that color and also shading, let us cover one last point about map symbolization. The rules around using color and also shading are various for nominal matches higher-level data (ordinal, interval, and ratio). If you are mapping nominal-level data, the categories have actually no certain order, and also you more than likely want come maximize the contrast between categories. Land uses, for example, must be depicted so that you deserve to separate urban, suburban, forest, and pasture, or every little thing categories you include on the map.

Ordinal, interval or proportion data must be mapped differently. Here there is a identify ordering that categories. To use the temperature map again, we have actually a tendency from warm to cold in the zones we portray. We want the map leader to immediately appreciate this progressive trend in the data. Therefore we select an bespeak of color or icons that conveys this consistent trend in the data, for example: red-orange-yellow-green-blue-violet.

See more: How To Read Ounces On A Digital Scale For Accurate Measurement

Many civilization make the wrong of reasoning they should pick colors that maximize contrast in between categories, also with ordinal or higher-level data. Beware this mistake! girlfriend may have the ability to pick the end categories quickly with this approach, yet you destroy the impression that a trend in the data.