Question

the uncertainty is about 0.01 mm
exercise: compare the uncertainty between 0.25 km and 0.250 km

Explanation:

Step1: Determine significant figures and uncertainty for 0.25 km

0.25 km has 2 significant figures. The last digit 5 is in the hundred - ths place in terms of km. 1 km = 1000 m and 1 m = 1000 mm, so 1 km=1000000 mm. The uncertainty for a measurement with 2 significant figures like 0.25 km is ±0.01 km. Converting to mm, 0.01 km = 0.01×1000000 mm=10000 mm.

Step2: Determine significant figures and uncertainty for 0.250 km

0.250 km has 3 significant figures. The last digit 0 is in the thousand - ths place in terms of km. The uncertainty for a measurement with 3 significant figures like 0.250 km is ±0.001 km. Converting to mm, 0.001 km = 0.001×1000000 mm = 1000 mm.

Step3: Compare the uncertainties

Since 10000 mm>1000 mm, the uncertainty of 0.25 km is greater than the uncertainty of 0.250 km.

Answer:

The uncertainty of 0.25 km is greater than the uncertainty of 0.250 km.