express the following statement scale as RF scale (i) 0.5cm to represent 2metres (ii) 2cm to. represent 4kilometre (iii) 2inches to represent 1mile (iv) 1.5cms to represent 2.5kilometres.
1. Express the following statement scale as RF scale
i) 0.5cm to represent 2metres.
ii) 2cm to represent 1kilometre
iii) 2inches to represent 1kilolometre
iv) 1.5cmto represent 2.5kilometre
To express the given statements on an RF (Representative Fraction) scale, we need to establish the ratio between the measurements on the map (in centimeters or inches) and the corresponding actual distances (in meters or kilometers).
(i) 0.5 cm representing 2 meters:
To determine the RF scale, we divide the map distance by the actual distance:
RF scale = Map distance / Actual distance
RF scale = 0.5 cm / 200 cm (as 1 meter = 100 cm, and 2 meters = 2 x 100 cm = 200 cm)
Simplifying the above expression:
RF scale = 0.5 cm / 200 cm = 1/400
Therefore, the expression on the RF scale for 0.5 cm representing 2 meters is 1/400.
(ii) 2 cm representing 4 kilometers:
Following the same process as above:
RF scale = 2 cm / (4,000 cm) (as 1 kilometer = 1,000 meters and 4 kilometers = 4 x 1,000 meters = 4,000 meters)
Simplifying the above expression:
RF scale = 2 cm / 4,000 cm = 1/2,000
Therefore, the expression on the RF scale for 2 cm representing 4 kilometers is 1/2,000.
(iii) 2 inches representing 1 mile:
Converting inches to meters, we have:
1 inch = 0.0254 meters (approximately)
RF scale = 2 inches / (1 mile) (as 1 mile = 1,609.34 meters)
RF scale = 2 x 0.0254 meters / 1,609.34 meters
Simplifying the above expression:
RF scale = 0.0508 / 1,609.34
RF scale ≈ 1/31,622
Therefore, the expression on the RF scale for 2 inches representing 1 mile is approximately 1/31,622.
(iv) 1.5 cm representing 2.5 kilometers:
Following the same process as above:
RF scale = 1.5 cm / (2,500 cm) (as 1 kilometer = 1,000 meters and 2.5 kilometers = 2.5 x 1,000 meters = 2,500 meters)
Simplifying the above expression:
RF scale = 1.5 cm / 2,500 cm = 1/1,667
Therefore, the expression on the RF scale for 1.5 cm representing 2.5 kilometers is 1/1,667.
To express the given statements on the RF (Representative Fraction) scale, we need to determine the ratio of the representative lengths to the actual lengths. The RF scale represents this ratio.
(i) 0.5cm represents 2 meters:
To find the RF scale for this statement, we need to determine the ratio of the representative length (0.5cm) to the actual length (2m):
RF scale = Representative length / Actual length
RF scale = 0.5cm / 2m
Since both values need to be in the same unit, we convert 2 meters to centimeters:
1 meter = 100 centimeters
2 meters = 2 * 100 centimeters = 200 centimeters
Now, we can calculate the RF scale:
RF scale = 0.5cm / 200cm
RF scale = 1/400
Therefore, the RF scale for this statement is 1/400.
(ii) 2cm represents 4 kilometers:
First, we convert 4 kilometers to centimeters:
1 kilometer = 100,000 centimeters
4 kilometers = 4 * 100,000 centimeters = 400,000 centimeters
Now, we can calculate the RF scale:
RF scale = 2cm / 400,000cm
RF scale = 1/200,000
Therefore, the RF scale for this statement is 1/200,000.
(iii) 2 inches represents 1 mile:
First, we convert 1 mile to inches:
1 mile = 63,360 inches
Now we can calculate the RF scale:
RF scale = 2 inches / 63,360 inches
RF scale = 1/31,680
Therefore, the RF scale for this statement is 1/31,680.
(iv) 1.5cm represents 2.5 kilometers:
First, we convert 2.5 kilometers to centimeters:
1 kilometer = 100,000 centimeters
2.5 kilometers = 2.5 * 100,000 centimeters = 250,000 centimeters
Now we can calculate the RF scale:
RF scale = 1.5cm / 250,000cm
RF scale = 1/166,667
Therefore, the RF scale for this statement is 1/166,667.