Calculate the RF when the Verbal scale is 4 cm to 1 km
The correct answer and explanation is:
Okay, let’s calculate the Representative Fraction (RF) from the verbal scale 4 cm to 1 km.
The Correct Answer:
The RF is 1:25,000.
Explanation:
The Representative Fraction (RF) is a map scale that expresses the relationship between a distance on the map and the corresponding distance on the Earth’s surface as a ratio or fraction. For an RF to be meaningful, both the map distance and the ground distance must be expressed in the same units.
The given verbal scale is “4 cm to 1 km”. This means that a length of 4 centimeters on the map represents an actual distance of 1 kilometer on the ground.
To calculate the RF, we need to convert the ground distance (1 km) into the same unit as the map distance (centimeters). We know the following conversion factors:
- 1 kilometer (km) = 1,000 meters (m)
- 1 meter (m) = 100 centimeters (cm)
Therefore, to convert 1 kilometer to centimeters, we multiply:
1 km = 1,000 m * 100 cm/m = 100,000 centimeters.
Now we can express the scale as a ratio of map distance to ground distance using the same units:
Map distance : Ground distance
4 cm : 100,000 cm
The RF is typically written with a numerator of 1. To achieve this, we divide both sides of the ratio by the map distance (4):
(4 cm / 4) : (100,000 cm / 4)
1 cm : 25,000 cm
When the units are the same, they cancel out, leaving a dimensionless ratio or fraction. The Representative Fraction is therefore 1:25,000 or 1/25,000. This means that any unit of measurement on the map represents 25,000 of the same units on the ground.