Converting Between Scale Types of Historic & Modern Maps, page 3

Converting Representative Fraction (RF)/Ratio Scale to Lexical Scale

English and Metric Measures of Length to use:

1 inch (in) = 2.54 centimeters
1 centimeter (cm) = 0.39 inch
1 foot (ft) = 12 inches = 30.5 centimeters = 0.3 meter
1 yard (yd) = 36 inches = 3 feet = 91.44 centimeters = 0.9 meter
1 meter (m) = 100 centimeters = 39.37 inches = 3.28 feet = 1.09 yards
1 mile (mi) = 63,360 inches = 5,280 feet = 1,760 yards = 1.609 kilometers
1 nautical mile = 1,852 meters = 1.852 kilometers
1 kilometer (km) = 1,000 m = 100,000 cm = 1,094 yards = 0.6 mile

NOTE: When you carry out any calculation with fractions, make sure that all units in equation are cancelled correctly. If necessary, invert the RF for that purpose.

It is necessary to choose appropriate units to convert into. Most lexical scales are either "one inch represents X miles," or "one centimeter represents X kilometers." These are relatively easy to do, since it means only that we convert the denominator of our Representative Fraction (RF) to the larger units.

1. IN METRIC UNITS

For example, you have to convert from RF/Ratio Scale of 1:50,000 to a Lexical Scale:

Equation for Converting Representative Fraction (RF) Scale to Lexical Scale

or "1 centimeter represents 500 meters"

In a similar way you can determine Lexical Scales from the following RF/Ratio Scales:

Equation for

or "1 centimeter represents 240 meters"

Equation for

or "1 centimeter represents 100 meters"

Equation for

or "1 centimeter represents 2.5 kilometers"

Equation for

or "1 centimeter represents 20 kilometers"

You can convert RF Scale to Lexical Scale quicker by simply dividing the denominator of RF by 100 if you want a lexical scale to be expressed in meters. As they say in military, "you take two zeroes out of denominator":

Equation for

or "1 centimeter represents 500 meters"

If you want a lexical scale to be expressed in kilometers, "you take five zeroes out of denominator" or divide the denominator value by 100,000:

Equation for

or "1 centimeter represents 10 kilometers"

2) IN ENGLISH UNITS

For example, you have to convert from RF/Ratio Scale of 1:25,000 to a Lexical Scale:

Equation for Converting Representative Fraction (RF) Scale to Lexical Scale in English Units

Converting Representative Fraction (RF) Scale to Lexical Scale in English Units

or "1 inch represents 0.39 mile"

To express a Lexical Scale in yards:

Equation for Converting Representative Fraction (RF) Scale to Lexical Scale in Yards

Converting Representative Fraction (RF) Scale to Lexical Scale in Yards

or "1 inch represents 694 yards"


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