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What is the R.F for scale is 1 cm = 4.5 m
1/450
1/4500
1/45000
1/450000
1/450
Given: The scale is given as 1 cm = 4.5 m.
The scale is given as 1 cm = 4.5 m.
R.F.=Actual Ground DistanceMap Distance
Identify the formula for R.F.
Representative Fraction (R.F.) is defined as the ratio of the map distance to the corresponding ground distance in the same units.
R.F.=Ground DistanceMap Distance
Convert units to a common base
The given scale is 1 cm=4.5 m. We must convert the ground distance into centimeters: 4.5 m=4.5×100 cm=450 cm.
4.5 m=450 cm
Calculate the R.F.
Substitute the values into the formula: R.F.=450 cm1 cm. The units cancel out, leaving a unitless ratio.
R.F.=4501
A is correct because the ratio of map distance to ground distance after converting both to centimeters results in 1/450.
In surveying and cartography, always ensure that both numerator and denominator in R.F. calculations are in the same units to ensure a dimensionless fraction.