If representative fraction of a map is 1:16000000, then its scale is
- A1 cm = 1600 km
- B1 cm = 160 kmCorrect
- C1 cm = 16 km
- DNone of these
Solution
Concept
Scale of a map is expressed as the ratio of map distance to ground distance, often represented as a Representative Fraction (RF).
Formula
RF = Map Distance / Ground Distance
Step-by-step solution
1. Write down the given Representative Fraction: RF = 1 : 16,000,000. 2. Interpret the ratio: 1 cm on the map represents 16,000,000 cm on the ground. 3. Convert cm to km knowing that 1 km = 100,000 cm. 4. Ground distance = 16,000,000 / 100,000 = 160 km. 5. Thus, the scale is 1 cm = 160 km.
Explanation
The Representative Fraction (RF) is given as 1:16,000,000, which means 1 unit on the map represents 16,000,000 units on the ground. Converting centimeters to kilometers (since 1 km = 100,000 cm), 16,000,000 cm becomes 160 km. Therefore, the scale is 1 cm = 160 km.
Why the other options are wrong
A: 1 cm = 1600 km results from a miscalculation of zeros. C: 1 cm = 16 km results from missing one zero during conversion. D: None of these is incorrect since option B is correct.
Shortcut
To convert centimeters in RF to kilometers, divide the ground units by 100,000 (remove 5 zeros).
Common mistake
Confusing conversion factors between centimeters and kilometers, leading to incorrect placement of decimal points.
Correct answer: B) 1 cm = 160 km