A map of a certain area is drawn on a sheet. The distance on the map is 1 dm and that on the ground is 5 km. The representative fraction for the given data is _____________.
Correct Answer:
B. 1 / 50000
📝 Detailed Explanation: Calculating the Representative Fraction (R.F.)
The Representative Fraction (R.F.) is a unitless ratio that shows the relationship between a distance on a map and the corresponding distance on the ground. It is always expressed in the form 1 / X or 1:X.
The Formula
R.F. = (Distance on the Map) / (Distance on the Ground)
The Golden Rule: To calculate the R.F. correctly, both the map distance and the ground distance MUST be converted to the exact same unit before applying the formula.
Step-by-Step Calculation
- Identify the given data:
- Map Distance = 1 dm (decimetre)
- Ground Distance = 5 km (kilometres)
- Convert both distances to a common unit. Let's use centimetres (cm) as it is a convenient base unit.
- Convert Map Distance: 1 dm = 10 cm
- Convert Ground Distance:
5 km = 5 × 1,000 meters
5,000 meters = 5,000 × 100 centimetres = 500,000 cm
- Apply the R.F. formula with the converted units:
R.F. = (10 cm) / (500,000 cm)
- Simplify the fraction to the standard 1/X format:
Divide both the numerator and the denominator by 10.
R.F. = 1 / 50,000
💡 Key Concepts for Students
- Unit Consistency is Everything: The most common mistake in R.F. calculations is failing to convert both measurements to the same unit. Always double-check your conversions.
- Understanding the Ratio: An R.F. of 1/50,000 means that 1 unit of any length (e.g., 1 inch, 1 cm, 1 mm) on the map represents 50,000 of those same units on the ground.