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English system use inch, yard, and mile in measurement.
Advantages :
(i) This is very simple method which is understood even by a common man.
(ii) It requires little time to express this scale.
(iii) It gives correct idea about distance.
Disadvantages :
(i) It can be understood only by those who are familiar with the unit of measurement used. For example, if we say that the scale of a map is 1 cm : 1 km, it would be understood by only that person who is familiar with the metric system of measurement.
(ii) When a map is reduced or enlarged from the original, the scale does not remain the same. This creates problems in measurement.
5 cm represents
= 10 km or 1000000 cm
1 cm represents = 1000000 ÷ 5
=200000
R. F. : 1 : 200000
2.
5 cm represents
= 10 km or 1000000 cm
1 cm represents = 1000000 ÷ 5
=200000
R. F. : 1 : 200000
3.
1' represents = 1 yard or 36'
1' represents =36'
R. F. : 1 : 36
4.
l cm represents= 100 metres
1 cm represents = 100 metres or 10000 cm
R. F. : 1 : 10000
2. Without a scale, a map is simply a diagram or sketch. A map is meaningless without a scale.
3. We can measure the distance between two points on the map without actually going to the field.
4. With the help of a scale, the area can be calculated.
5. A certain length can be measured from the linear scale.
What is Representative Fraction ? Give its advantages and disadvantages.
Representative Fraction is also known as Numerical Function. In this case, the ratio existing between the length on the map and actual length on the ground is indicated by a fraction whose numerator is always 1. This fraction is usually abbreviated as R. F. Thus, Representative Fraction (R.F.)
The most important point to be noted in this connection is that the unit of measurement of distances in numerator and denominator is the same. For example, if we say the R.F. of a map is 1/1,00,000 or 1: 1,00,000, it means that one unit on the map represents 1,00,000 units on the ground. If the unit of measurement is centimetre, we will say that 1 centimetre on the map represents 1,00,000 centimetres on the ground. If, however, the unit of measurement is an inch, then we will say that 1 inch on the map represents 1,00,000 inches on the ground.
Advantages: Since it is only a fraction and is indented of any particular unit of a measurement, it can be used in all the countries. If the R.F. of a map is 1: 1,00,000 to a Britisher, it would mean that 1" on the map represents 1,00,000 inches on the ground. Similarly, to a Frenchman, it would mean that 1 cm on the map represents 1,00,000 inches on the ground and to a Russian, 1 verst on the map represents 1,00,000 versts on the ground. It is also termed as International Scale or Natural Scale. It has become a very popular method of expressing the scale.
Disadvantages :
Advantages : (i) Distances can easily be measured with the help of linear scale.
(ii) If the map is photographically enlarged or reduced, the linear scale is also enlarged or reduced in the same ratio and remains true to the map.
Disadvantages : (i) Like statement of scale, this scale can be used by those who are familiar with the unit of measurement used in the scale.
(ii) It requires time and proficiency in drawing a graphic scale.
The R.F. of a map is 1 : 5,00,000. Convert it into statement of scale showing kilometres.
The given R.F. is 1: 5,00,000 cm
This means that 1 cm of the map represents 5,00,000 cm on the ground.
Hence 1 cm : 5,00,000 cm
or 1 cm = 5,00,000/1,00,000 km
or 1 cm = 5 km.
Therefore statement of scale is 1 cm: 5 km.
The R.F. of a map is 1 :3,16,800. Convert it into statement of scale for showing miles.
The given R.F. is 1: 3,16,800. This means that one inch on the map represents 3,16,800 inches on the ground, or 1 inch: 3,16, 800 inches or or 1 inch: 5 miles
Hence, statement of scale = 1 inch : 5 miles
Draw a plain scale for a map whose scale is 1 cm : 10 km.
1 cm on the map represents 10 km on the ground.
15 cm on the map represents on the ground
= 10 × 15 = 150 km.
(The normal length of scale should be 15 cm) 150 km is a round number. Therefore we not select any other number.
Scale 1 cm : 10 km.
Construction. Draw a line 15 cm long. Divide it into 15 primary divisions. Each division represents 10 km. Sub-divide the left-hand divisions into five secondary divisions, each showing a distance of 2 kms.
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Draw a plain scale for a map whose scale is 1 inch : 7 miles.
1 inch represents a distance = 7 miles
6 inch represents a distance = 7 × 6 = 42 miles
But 42 miles is not a round number. Select a round number of 45 miles. Find out the map distance for a distance of 45 miles.
7 miles are represented by = 1 inch
1 mile is represented by = 1/7 inch
45 miles are represented by = 1/7 × 45
= 6.4 inches approximately.
Scale 1 Inch: 7 Miles
Construction. Draw a line 6.4 inches long. Divide it into nine equal parts. Each part showing 5 miles. Sub-divide the left-hand part into 5 divisions, each will show a distance of 1 mile.
Calculate the R.F. when the scale is one centimetre to one kilometre or 1 cm=l km.
The scale of the map is 1 cm = 1 km. or 1 cm 100,000 cm since 1 km = 1,00.000 cm.
Draw a plain scale to show yards for a map whose scale is 4 inches : 1 mile.
Scale 4 inches: 1 mile
4 inches on the map represent =1 = 1760 yards
1 inch on the map represents = 1760/4 yards
6 inches on the map represent =
But 2640 yards is not a round number. Select a round number of 3000 yards.
1760 yards are represented by = 4 inches
3000 yards are represented by
Construction: Draw a line 6.8 inches long. Divide it into 6 equal parts each showing 500 yards. Sub-divide the left-hand part into 5 equal divisions. Each will show 100 yards.
1' represents 2 miles.
4. 1 cm represents = 50000 cm or 500 metres.
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