1.5.3 - Analysis of the Limitation of another Ruler
The diagram below shows the measurement of the length of the same
blue bar using a ruler with 0.1 cm as its finest division.
Using this ruler, the length the blue bar can be recorded to more
accuracy, 2.34 cm.
In Section
1.6, you will learn that this measurement has 3 significant
figures.
Let's analyze this measurement:
Upon inspection of the ruler, we observe that the finest
division is a 0.1 cm division.
We can always make an estimate of a reading to within the finest division.
Therefore, to the best of my judgement, I conclude that this particular ruler
is able to provide a reading accuracy to +/- 0.02 cm.
(Note: A plus or minus 0.02 cm reading accuracy means that a length measurement
using this ruler will contain uncertainty in the second decimal place.)
The end of the blue bar is between the 2.3
cm and the 2.4 cm mark. We can estimate that the blue bar exceeds 2.3 cm mark
by approximately 0.04 cm.
The length measurement is determined to be 2.34
cm.
The digit '2' and '3' are certain figures. The
digit '4' is an uncertain figure, or an estimate
in the measurement. Therefore, this length measurement has 3
significant figures. (Note: This measurement is accurate to 2.34
+/- 0.02 cm (i.e. 2.34 plus or minus 0.02 cm). It means that using
this ruler, the length of the blue bar is between
2.32 cm to 2.36 cm.)
