A digital caliper is used to measure the 28.50 mm width of a plastic ruler. The digital caliper reads to the nearest 0.01 mm.

Question 8

A digital caliper is used to measure the 28.50 mm width of a plastic ruler. The digital caliper reads to the nearest 0.01 mm.

What is the correct way to record this reading?

A 0.02850 ± 0.01 m

B 0.0285 ± 0.001 m

C (2.850 ± 0.001) ×10^-2 m

D (2.850 ± 0.001) ×10^-3 m

Reference: Past Exam Paper – June 2014 Paper 13 Q6

Solution:

Answer: C.

1 mm = 10^-1 cm           and      1 mm = 10^-3 m

0.01 mm = 0.01×10^-1 cm = 0.01×10^-3 m

By writing 0.001, we need to divide 0.01 by 10. This should be removed from the 10^-3 which now becomes 10^-2.

So, 0.01 mm = 0.001×10^-2 m

Note that when writing readings with uncertainties, the uncertainty should always be given to 1 significant figure (here it is the ‘one’ in 0.001) and the reading should be given to the same number of decimal places as the uncertainty (here, it is 3 d.p as in 2.850).