A. What is a Scale?
The Scale of a Map is the fixed mathematical ratio between the distance measured on the map and the corresponding actual horizontal distance on the ground:
$$\mathbf{\text{Scale} = \frac{\text{Distance on Map}}{\text{Actual Distance on Ground}}}$$B. Three Methods of Expressing Scale:
- Statement of Scale (Verbal Scale): Expressed in simple words (e.g., *$1\text{ cm to } 5\text{ km}$*).
Limitation: Requires specific knowledge of the language and units (metric vs imperial).
- Representative Fraction (RF): A dimensionless numerical fraction or ratio where the numerator is always $1$ (representing map distance) and the denominator represents the ground distance in the exact same unit of measurement:
$$\mathbf{\text{RF} = \frac{\text{Map Distance}}{\text{Ground Distance}}}$$
- Conversion Example: Convert "$1\text{ cm to } 2.5\text{ km}$" into RF: $$\text{Ground Distance} = 2.5\text{ km} = 2.5 \times 100,000\text{ cm} = 250,000\text{ cm}$$ $$\mathbf{\text{RF} = 1 : 250,000 \quad \text{or} \quad \frac{1}{250,000}}$$
- Linear / Graphical Scale: A straight line divided into equal primary and secondary graduated units showing real kilometers or miles directly.
Supreme Advantage: If a map is photographically enlarged or reduced, the linear scale expands or contracts proportionally, keeping the scale measurement strictly accurate!