Final answer:
A map scale is expressed as a representative fraction or verbal description, and it is used to calculate the actual distance between two points. To determine actual distance, multiply the map distance by the scale's denominator; to find the RF, create a proportion with the known distances.
Step-by-step explanation:
When working with maps, it is crucial to understand the concept of a map scale, which is the ratio of a distance on the map to the actual distance on the ground. This can be expressed as a representative fraction (RF), such as 1:250,000, or verbally, for instance, '1 inch on the map represents 250,000 inches on the ground'.
To calculate the actual distance between two points using a given map scale:
Convert the map distance to the same units as the RF if necessary.
Multiply the map distance by the RF denominator to find the actual ground distance.
For instance, if two places are 8 inches apart on a map with a scale of 1:250,000, the actual distance is calculated as follows:
8 inches (on the map) * 250,000 (RF denominator) = 2,000,000 inches on the ground
Since there are 63,360 inches in a mile, we divide the result by 63,360 to convert it to miles:
2,000,000 inches / 63,360 inches/mile = 31.55 miles (actual distance)
To find the fractional map scale (RF) if you know the actual distance and map distance:
Create a proportion. For example, if two cities are 10 inches apart on a map and 20 miles (1,267,200 inches) apart in reality, the RF is calculated as:
10 inches (on the map) / 1,267,200 inches (on the ground) = 1 / 126,720 (RF)