If the scale of a map is 1 cm = 1 km, then its representative fraction would be
- A1:100000Correct
- B100000:1
- C10000:1
- D1:10000
Solution
Concept
Representative Fraction (RF) is a dimensionless ratio expressing the scale of a map, where both numerator and denominator are expressed in the same unit of length.
Formula
RF = Map Distance / Ground Distance
Step-by-step solution
1. Identify the given scale: 1 cm on map = 1 km on ground. 2. Convert both quantities into the same unit (centimeters). We know that 1 km = 1,000 m = 100,000 cm. 3. Write the ratio as RF = 1 cm / 100,000 cm. 4. Simplify to obtain the representative fraction: 1:100,000.
Explanation
Representative Fraction (RF) is the ratio of the map distance to the corresponding ground distance in the same units. Since 1 km = 100,000 cm, 1 cm on the map representing 1 km on the ground gives an RF of 1 / 100,000 or 1:100,000.
Why the other options are wrong
B: 100000:1 means 100000 cm on map represents 1 cm on ground, which is reverse. C: 10000:1 is an incorrect conversion factor (corresponds to 1 cm = 100 m). D: 1:10000 represents a scale of 1 cm = 100 m.
Shortcut
Remember that 1 km equals 100,000 cm, so directly replace 'km' with '100,000 cm' to get 1:100,000.
Common mistake
Confusing the order of numbers and writing 100,000:1 instead of 1:100,000, or forgetting conversion factors between kilometers and centimeters.
Correct answer: A) 1:100000