A 2-km baseline is measured with an electronic total station. If the instrument accuracy is 5 mm + 5 ppm, what is the accuracy of the measured distance to the nearest thousandth?

Get ready for the Geodesy Board Exam with flashcards and multiple choice questions, complete with hints and explanations. Ace your test!

Multiple Choice

A 2-km baseline is measured with an electronic total station. If the instrument accuracy is 5 mm + 5 ppm, what is the accuracy of the measured distance to the nearest thousandth?

The test uses instrument accuracy expressed as a fixed part plus a proportional part: 5 mm + 5 ppm of the distance. For a baseline of 2 km (2000 m), the ppm part is 5 × 10^-6 × 2000 m = 0.01 m (10 mm). The fixed part is 5 mm, so the total absolute error is 5 mm + 10 mm = 15 mm = 0.015 m. The relative accuracy is this error divided by the distance: 0.015 m / 2000 m = 7.5 × 10^-6, which is about 1 in 133,000. Therefore the closest option matches 1/133000.

The test uses instrument accuracy expressed as a fixed part plus a proportional part: 5 mm + 5 ppm of the distance. For a baseline of 2 km (2000 m), the ppm part is 5 × 10^-6 × 2000 m = 0.01 m (10 mm). The fixed part is 5 mm, so the total absolute error is 5 mm + 10 mm = 15 mm = 0.015 m.

The relative accuracy is this error divided by the distance: 0.015 m / 2000 m = 7.5 × 10^-6, which is about 1 in 133,000. Therefore the closest option matches 1/133000.

More practice questions