What is the meaning of "Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit".?

1 Answer
Aug 15, 2017

It means precision is ± 0.1 mm


This is an issue about precision. Every measurement has an inherent uncertainty. The better your measuring instrument the higher your precision and that means you can state the measurement with more significant figures. Some simple and common examples for length measurements:
Metre rule: ± 1 mm
Vernier calliper: ± 0.1mm
Micrometer: ± 0.01 mm
The micrometer measures to the highest precision out of the instruments above.

In the case of the question the metre rule is used so that its measurement is more precise than I have stated above as it is to the nearest tenth of a millimetre, i.e. ± 0.1 mm.

The question states that the last significant figure is to the tenth of a millimetre. A tenth of a millimetre is 0.1 mm, so every measurement must be written to 1 d.p. if mm is used as the prefix and unit. But also one tenth of a millimetre is 0.01 cm, so every measurement written in cm must be written to 2 d.p.. This is exactly what ± 0.1 mm and ± 0.01 cm signify.

Here are some example measurements to give it some context:
① The width of a table which is exactly 70 cm across. The measurement should be stated as 700.0 mm or 70.00 cm or 0.7000 m (as every measurement must be stated to the precision which is 0.1 mm). Notice that every number I have stated is 4 significant figures regardless of the prefix used.
② The width of a mobile phone is 6.71 cm. The measurement should be stated as 67.1 mm or 6.71 cm or 0.0671 m. These are all 3 s.f. and all written to the nearest tenth or a millimetre.