Express the following statement as RF scale
i)0.5cm to represent 2 metres
ii)2cm to represent 4 kilometre
iii)2 inches to represent 1 milie
i) 1:400
ii) 1:200,000
iii) 1:63,360
Express the following RF scale in cms to kms
i)1:1000000
ii)1:77777
iii)1:133333
iv)1:9000
v)1:6000000
i) 1 cm represents 10 kms
ii) 1 cm represents 777.77 m (or 0.77777 km)
iii) 1 cm represents 1.33333 kms
iv) 1 cm represents 90 m (or 0.09 km)
v) 1 cm represents 60 kms
0.5 cm = 0.005 m
so
0.005 m / 2 m = 1 m / x m
x = 2 / .005 = 400
so
1/400
========
2 cm = 0.02 m
4 km = 4,000 m
0.02 / 4000 = 1/x
x = 4000/0.02 = 200,000
so
1/200,000
etc
These calculations are correct and result in the correct RF scale for each scenario.
In order to express the given statements as RF (Representative Fraction) scales, we need to find the ratio of the given measurements to their corresponding distances on a map. The RF scale is expressed in the form of 1:n, where n is the ratio.
i) To express 0.5cm to represent 2 metres:
First, we need to find the ratio of map distance to actual distance:
0.5cm : 2 m
To convert cm to meters, we need to divide the 0.5cm by 100 since there are 100 centimeters in 1 meter:
0.005m : 2 m
Now, we can simplify this ratio:
0.005/2 = 0.0025
The RF scale for this statement would be 1:0.0025.
ii) To express 2cm to represent 4 kilometers:
Similar to the previous example, we need to find the ratio of map distance to actual distance:
2cm : 4 km
To convert cm to kilometers, we divide the 2cm by 100,000 since there are 100,000 centimeters in 1 kilometer:
0.00002 km : 4 km
Now, we simplify this ratio:
0.00002/4 = 0.000005
The RF scale for this statement is 1:0.000005.
iii) To express 2 inches to represent 1 mile:
Again, we need to find the ratio of map distance to actual distance:
2 inches : 1 mile
To convert inches to miles, we divide the 2 inches by 63,360 since there are 63,360 inches in 1 mile:
0.0000315 miles : 1 mile
Simplifying this ratio:
0.0000315/1 = 0.0000315
The RF scale for this statement is 1:0.0000315.
To express the given statements as RF scale, we need to determine the ratio between the actual distance (represented in meters, kilometers, or miles) and the scaled distance (represented in centimeters or inches). The scale ratio is expressed as a fraction or a ratio, where the numerator represents the scaled distance and the denominator represents the actual distance.
i) 0.5 cm to represent 2 meters:
To find the RF scale for statement (i), we need to determine the ratio between the scaled distance and the actual distance. Since the scaled distance is given as 0.5 cm and the actual distance is 2 meters, we can set up the ratio as follows:
Scaled distance (cm) / Actual distance (m) = RF scale
0.5 cm / 2 m = RF scale
Simplifying the ratio:
0.5 cm / 2 m = 1 cm / X m
Cross-multiplying and solving for X:
(0.5 cm) * (X m) = (2 m) * (1 cm)
0.5X = 2
X = 4
Therefore, the RF scale for statement (i) is 1:4. This means that 1 cm on the map represents 4 meters in reality.
ii) 2 cm to represent 4 kilometers:
For statement (ii), we can follow a similar approach. Given that the scaled distance is 2 cm and the actual distance is 4 kilometers:
Scaled distance (cm) / Actual distance (km) = RF scale
2 cm / 4 km = RF scale
Simplifying the ratio:
2 cm / 4 km = 1 cm / X km
Cross-multiplying and solving for X:
(2 cm) * (X km) = (4 km) * (1 cm)
2X = 4
X = 2
Hence, the RF scale for statement (ii) is 1:2. This means that 1 cm on the map represents 2 kilometers in reality.
iii) 2 inches to represent 1 mile:
Now, for statement (iii), let's determine the RF scale by considering that the scaled distance is 2 inches and the actual distance is 1 mile:
Scaled distance (inches) / Actual distance (miles) = RF scale
2 inches / 1 mile = RF scale
Simplifying the ratio:
2 inches / 1 mile = 1 inch / X miles
Cross-multiplying and solving for X:
(2 inches) * (X miles) = (1 mile) * (1 inch)
2X = 1
X = 1/2
Therefore, the RF scale for statement (iii) is 1:1/2 or simplified as 1:0.5. This means that 1 inch on the map represents 0.5 miles in reality.