A 2.5-km baseline is measured with an electronic total station. If the vendor's accuracy specification of the instrument is ± (5mm + 2ppm).calculate the accuracy of the measured distance to the nearest thousand.

• A. 1/255,000
• B. 1/245,000
• C. 1/240,000
• D. 1/250,000

Answer: (D)

The key idea is to combine a fixed error with a distance-proportional error and express the result as a ratio to the measured length. The distance is 2.5 km = 2,500,000 mm. The instrument’s accuracy is 5 mm plus 2 ppm of the distance, so the 2 ppm part is 2e-6 × 2,500,000 mm = 5 mm. Total absolute error = 5 mm + 5 mm = 10 mm. Expressing this as a ratio to the length gives 10 mm / 2,500,000 mm = 1/250,000. So the measurement is accurate to about one part in 250,000. This matches the given choice.