Representative Fraction is also known as Numerical Function. In this case, the ratio existing between the length on the map and actual length on the ground is indicated by a fraction whose numerator is always 1. This fraction is usually abbreviated as R. F. Thus, Representative Fraction (R.F.)

The most important point to be noted in this connection is that the unit of measurement of distances in numerator and denominator is the same. For example, if we say the R.F. of a map is 1/1,00,000 or 1: 1,00,000, it means that one unit on the map represents 1,00,000 units on the ground. If the unit of measurement is centimetre, we will say that 1 centimetre on the map represents 1,00,000 centimetres on the ground. If, however, the unit of measurement is an inch, then we will say that 1 inch on the map represents 1,00,000 inches on the ground.

Advantages: Since it is only a fraction and is indented of any particular unit of a measurement, it can be used in all the countries. If the R.F. of a map is 1: 1,00,000 to a Britisher, it would mean that 1" on the map represents 1,00,000 inches on the ground. Similarly, to a Frenchman, it would mean that 1 cm on the map represents 1,00,000 inches on the ground and to a Russian, 1 verst on the map represents 1,00,000 versts on the ground. It is also termed as International Scale or Natural Scale. It has become a very popular method of expressing the scale.

Disadvantages :

1. It is only a fraction in which no system of units is used. Hence, distances cannot be directly measured from it.
2. Whenever a map is photographically enlarged or reduced, the R.F. will no longer be true.
3. This is not easily understood by a common man.

Linear Scale : This is also known as Graphical Scale or Plain Scale. This is merely a straight line whose length is in certain proportion to the actual length on the ground. It is divided into primary and secondary division so that advantages and disadvantages can easily be read from it.

Advantages : (i) Distances can easily be measured with the help of linear scale.

(ii) If the map is photographically enlarged or reduced, the linear scale is also enlarged or reduced in the same ratio and remains true to the map.

Disadvantages : (i) Like statement of scale, this scale can be used by those who are familiar with the unit of measurement used in the scale.

(ii) It requires time and proficiency in drawing a graphic scale.

The given R.F. is 1: 5,00,000 cm

This means that 1 cm of the map represents 5,00,000 cm on the ground.

Hence 1 cm : 5,00,000 cm

or 1 cm = 5,00,000/1,00,000 km

or 1 cm = 5 km.

Therefore statement of scale is 1 cm: 5 km.

The given R.F. is 1: 3,16,800. This means that one inch on the map represents 3,16,800 inches on the ground, or 1 inch: 3,16, 800 inches or or 1 inch: 5 miles

Hence, statement of scale = 1 inch : 5 miles