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In a closed loop traverse of 1 km total length, the closing errors in departure and latitude are 0.3 m and 0.4 m respectively. The relative precision this traverse will be
- a)1:5000
- b)1:4000
- c)1:2000
- d)1:3000
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a closed loop traverse of 1 km total length, the closing errors in ...
Total closing error(c) 
Sum of latitude = 0.4 m
Sum of Departure = 0.3 m
C = 0.5m
Relative error of closure or Relative precision of this traverse = c/p
p ⇒ Perimeter of traverse = 1 km = 1000 m
Relative precision
Most Upvoted Answer
In a closed loop traverse of 1 km total length, the closing errors in ...
Relative precision can be calculated using the formula:
Relative Precision = Closing Error / Total Length
Given:
Closing Error in Departure = 0.3 m
Closing Error in Latitude = 0.4 m
Total Length = 1 km = 1000 m
Calculating the relative precision in departure:
Relative Precision in Departure = 0.3 m / 1000 m = 0.0003
Calculating the relative precision in latitude:
Relative Precision in Latitude = 0.4 m / 1000 m = 0.0004
Comparing the relative precision in departure and latitude, we can see that the value for latitude is greater. Therefore, the relative precision for this traverse is determined by the value for latitude.
The relative precision is given by the reciprocal of the value for latitude. This is because the relative precision represents the factor by which the measured distances have been reduced or enlarged due to errors. So, a higher value for relative precision indicates a smaller reduction or enlargement of distances and therefore a higher level of accuracy.
In this case, the relative precision in latitude is 0.0004. Taking its reciprocal, we get:
Reciprocal of 0.0004 = 1 / 0.0004 = 2500
Hence, the relative precision for this traverse is 1:2500. However, since the question asks for the relative precision in terms of a ratio, we can simplify the ratio to its lowest terms:
1:2500 = 1 / 1000: 2500 / 1000 = 1:2.5
Therefore, the relative precision for this traverse is 1:2000 (option C).
Relative Precision = Closing Error / Total Length
Given:
Closing Error in Departure = 0.3 m
Closing Error in Latitude = 0.4 m
Total Length = 1 km = 1000 m
Calculating the relative precision in departure:
Relative Precision in Departure = 0.3 m / 1000 m = 0.0003
Calculating the relative precision in latitude:
Relative Precision in Latitude = 0.4 m / 1000 m = 0.0004
Comparing the relative precision in departure and latitude, we can see that the value for latitude is greater. Therefore, the relative precision for this traverse is determined by the value for latitude.
The relative precision is given by the reciprocal of the value for latitude. This is because the relative precision represents the factor by which the measured distances have been reduced or enlarged due to errors. So, a higher value for relative precision indicates a smaller reduction or enlargement of distances and therefore a higher level of accuracy.
In this case, the relative precision in latitude is 0.0004. Taking its reciprocal, we get:
Reciprocal of 0.0004 = 1 / 0.0004 = 2500
Hence, the relative precision for this traverse is 1:2500. However, since the question asks for the relative precision in terms of a ratio, we can simplify the ratio to its lowest terms:
1:2500 = 1 / 1000: 2500 / 1000 = 1:2.5
Therefore, the relative precision for this traverse is 1:2000 (option C).
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