Which of the following scales is the smallest one?
🗺️ Understanding Map Scales
A map scale represents the ratio of a distance on the map to the corresponding distance on the ground. To compare different scales, we must convert them to a standard, unitless format called the Representative Fraction (RF).
The RF is always expressed as 1 : (some number) or 1 / (some number). The key principle is: the smallest scale has the largest denominator in its RF. A smaller scale covers a larger area but shows less detail.
🔬 Detailed Analysis of the Options
To find the smallest scale, let's convert each option into its Representative Fraction (RF) by ensuring both the map distance and ground distance are in the same unit (e.g., centimeters).
D. 1 cm = 5000 m
This is the correct answer. Let's convert the ground distance to centimeters:
- Ground distance = 5000 m
- Since 1 m = 100 cm, Ground distance = 5000 × 100 cm = 500,000 cm.
- This means 1 cm on the map represents 500,000 cm on the ground.
- RF = 1 / 500,000. This denominator is the largest among all options, making it the smallest scale.
A. 1 cm = 50 m
This is incorrect. Converting to RF:
- Ground distance = 50 m = 50 × 100 cm = 5,000 cm.
- RF = 1 / 5,000.
B. RF = 1/50000
This is incorrect. The scale is already given in RF form: 1 / 50,000.
C. 4 : 200000
This is incorrect. To convert this ratio to RF, we make the first number '1' by dividing both sides by 4:
- 4 / 4 : 200000 / 4
- 1 : 50,000
- RF = 1 / 50,000. This is the same scale as option B.
📊 Summary: Comparing the Scales
| Option | Original Form | Calculation (to cm) | Representative Fraction (RF) |
|---|---|---|---|
| A | 1 cm = 50 m | 1 cm on map = 50 x 100 cm on ground | 1 / 5,000 |
| B | RF = 1/50000 | N/A (already in RF) | 1 / 50,000 |
| C | 4 : 200000 | Divide both by 4 => 1 : 50000 | 1 / 50,000 |
| D | 1 cm = 5000 m | 1 cm on map = 5000 x 100 cm on ground | 1 / 500,000 |
💡 Study Tips
- Smallest Scale = Largest Denominator: This is the golden rule. The bigger the number after the "1 :", the smaller the scale.
- Units Must Match: Always convert map and ground distances to the same unit before creating the RF. Centimeters are commonly used.
- Think Big vs. Small Area: A small-scale map (e.g., 1:500,000) shows a large area (like a state), while a large-scale map (e.g., 1:5,000) shows a small area (like a park) in greater detail.