express the following stetement scale as RF scale 0.5cm to represent 2metres
2cm to represent 4kilometre
2 inches to represent 1mile
1.5cms to represent 2.5kilometres
0.5cm
0.5cm to 2m
To express these statements on the RF (Representative Fraction) scale:
1. First, let's find the scale for the first statement:
Given: 0.5cm represents 2 meters
To find the scale, we need to determine how many meters are represented by 1 centimeter.
0.5cm represents 2 meters
So, 1 centimeter represents 2/0.5 = 4 meters.
Therefore, the scale for the first statement would be 1:400 (1cm represents 400cm).
2. Now, let's find the scale for the second statement:
Given: 2cm represents 4 kilometers
Similar to the previous statement, we need to determine how many kilometers are represented by 1 centimeter.
2cm represents 4 kilometers
So, 1 centimeter represents 4/2 = 2 kilometers.
Therefore, the scale for the second statement would be 1:200 (1cm represents 200cm).
3. Finally, let's find the scale for the third statement:
Given: 2 inches represents 1 mile
Since 1 inch is equal to 2.54 centimeters, we need to convert the given values to centimeters.
2 inches = 2 * 2.54cm = 5.08cm
Now, we can find the scale by determining how many centimeters are represented by 1 mile.
5.08cm represents 1 mile
So, 1 centimeter represents 1/5.08 = 0.196 miles.
Therefore, the scale for the third statement would be 1:0.196 (1cm represents 0.196 miles).
4. For the last statement, we are given:
1.5cm represents 2.5 kilometers
Similar to the previous statements, we need to find how many kilometers are represented by 1 centimeter.
1.5cm represents 2.5 kilometers
So, 1 centimeter represents 2.5/1.5 = 1.66 kilometers.
Therefore, the scale for the fourth statement would be 1:166 (1cm represents 166 meters).
To express the given statements on an RF (Representative Fraction) scale, we need to calculate the scale factor for each statement. The scale factor is the ratio of distance on the map to the actual distance on the ground.
1. Scale: 0.5cm represents 2 metres
To calculate the scale factor, we divide the distance on the map by the actual distance: 0.5cm / 2m.
Simplifying this ratio, we get 1cm / 4m, which can also be written as 1:400 (1 unit on the map represents 400 units on the ground).
2. Scale: 2cm represents 4 kilometres
Calculating the scale factor: 2cm / 4km.
Simplifying this ratio, we get 1cm / 2km or 1:200, meaning 1 unit on the map represents 200 units on the ground.
3. Scale: 2 inches represents 1 mile
Converting inches to centimeters: 2 inches = 2 * 2.54 cm/inch = 5.08 cm.
Calculating the scale factor: 5.08cm / 1 mile.
However, miles need to be converted to centimeters to maintain consistent units. Since 1 mile = 1.60934 km = 160934 cm, the scale factor becomes 5.08cm / 160934cm.
Simplifying this ratio, we get approximately 1:31688, meaning 1 unit on the map represents 31688 units on the ground.
4. Scale: 1.5cm represents 2.5 kilometres
Calculating the scale factor: 1.5cm / 2.5km.
Simplifying this ratio, we get 0.6cm / 1km, which can also be written as 1:1667, meaning 1 unit on the map represents 1667 units on the ground.
These are the representative fractions (RF scales) for the given statements:
1. 1:400
2. 1:200
3. 1:31688
4. 1:1667