ALE - Uncertainty Name ______________________
M. Davis
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Uncertainty in Measuring Length
In chemistry, you will be using measured numbers in lab, in exercises, and on tests and quizzes. The
number of digits, i.e. significant figures, reported for a numerical quantity conveys the quality of the
measurement or analysis to the reader. When recording data or calculating numerical values, the
precision of these values, which is represented by the number of digits, is vital information. In science
courses, you will use a meaningful number of digits in reporting your results. Laboratory measuring
instruments have their limits, just as your senses have their limits. One of your tasks, in addition to
learning how to use various measuring instruments properly, will be to correctly determine the precision
of the measuring devices that you use in the lab.
Distances are normally measured with a ruler. The limit of accuracy of a ruler is indicated by how
"precisely" you can read the length on that ruler’s scale—that is, how well you can estimate between
the marks. On the portion of the ruler shown in Figure1, the distance between the closest marks is 0.1
cm. The dotted line to the right of the meter stick is at a length of 6.65 cm. The last decim al place, the
hundredth’s place, in the measurement is estimated. Here is the key for determining the precision of
most measuring devices:
You can usually estimate to only one decimal place beyond the closest marks on any measuring
device!!
On the ruler in figure 1, the closest marks are 0.1 cm apart, so you can estimate to the hundredths place,
0.01 cm. However, when looking at a metric ruler in the real world, the smallest marks (i.e. millimeter
marks, mm) are so close that it is all we can do just to determine that the dotted line is between two of
them—about half way. Therefore, your best estimate of the position of the dotted line is 6.65
centimeters. We can say that the measuring instrument is readable to ±0.05 cm. The ±0.05 cm means
that your measurement may be off by as much as 0.05 cm above or below its true value. This value is
called the uncertainty or the precision of the instrument.
Figure 1. A portion of a metric ruler (the centimeter scale has been enlarged for ease in reading)
Key Questions
1. What is the smallest scale increment of the ruler shown in fig. 1, above?
2. What distance is represented by dotted line “a” in Figure 1? How much uncertainty is there
in this measurement?
3. What distance is represented by dotted line “b” in Figure 1? How much uncertainty is there
in this measurement?
