- #1

fog37

- 1,568

- 108

- TL;DR Summary
- Correctly reporting uncertainties that accumulate measuring longer lengths

Hello,

It is clear that as distance being measured increases, more graduations are needed to represent a unit of measure for such distance. Each graduation in a measuring device is subject to uncertainty and error, and these errors and uncertainties accumulate with the increase in the number of graduations. For example, the meter stick has an instrumental accuracy of 0.5 mm (half the graduation of 1 mm).

How would we report the uncertainty taking into account the concept described above, i.e. the larger the measurement the greater the error since we include mode graduation units causing the error to accumulate?

For example: ##2.30 \pm 0.05 cm##. Would the uncertainty still be ##0.05 cm## if the measured distance was ##55.00 cm##? Based on what I shared, it should be higher...How much higher? How do we determine that?

Thank YOU

It is clear that as distance being measured increases, more graduations are needed to represent a unit of measure for such distance. Each graduation in a measuring device is subject to uncertainty and error, and these errors and uncertainties accumulate with the increase in the number of graduations. For example, the meter stick has an instrumental accuracy of 0.5 mm (half the graduation of 1 mm).

How would we report the uncertainty taking into account the concept described above, i.e. the larger the measurement the greater the error since we include mode graduation units causing the error to accumulate?

For example: ##2.30 \pm 0.05 cm##. Would the uncertainty still be ##0.05 cm## if the measured distance was ##55.00 cm##? Based on what I shared, it should be higher...How much higher? How do we determine that?

Thank YOU