A 200-meter baseline distance is measured with an electronic total station. If the vendor's accuracy specification of the instrument is ±(5mm + 2ppm), the precision of the measured distance relative to the baseline is closest to which value?

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The distance measurement error combines a fixed bias and a length-dependent term. The total absolute error for a 200 m baseline is:

• fixed term: 5 mm

• proportional term: 2 ppm of the length = 2 × 10^-6 × 200 m = 0.0004 m = 0.4 mm

So the overall absolute error is 5.0 mm + 0.4 mm = 5.4 mm (0.0054 m).

To express how precise the measurement is relative to the baseline, convert the absolute error to a fraction of the baseline:

relative error = 5.4 mm / 200 m = 5.4 × 10^-3 m / 200 m = 2.7 × 10^-5.

The precision, commonly described as the reciprocal of the relative error, is about 1 / 2.7 × 10^-5 ≈ 37,000. So the measurement is about 1 part in 37,000. The closest choice reflects 1/37,000.