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?

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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?

Explanation:
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.

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