1 Skills, Methods, and the Nature of Physics - BC Science Physics 11

Combining
Measurements
Imagine that you have a laboratory bench that is 1.756 m long. The last digit (in italics)
is an estimate to the nearest millimetre. You might call it an uncertain digit. Perhaps a
truer measure might be 1.755 m or 1.757 m. Often you must estimate the last digit in a
measurement when you guess what a reading is between the smallest divisions on the
measuring scale. This is true whether you are using a metre stick, a graduated cylinder, a
chemical balance, or an ammeter.
Adding or Subtracting Measurements
Now imagine that you decide to add some thin plastic trim to the two ends of your
bench. The trim has a width of 2.2 mm, which is 0.0022 m. What is the total length of the
bench with the new trim added?
You add the widths of the two trimmed edges to the original length of the bench,
like this:
1.756 m
0.0022 m
0.0022 m
1.7604 m = 1.760 m
There is no point in carrying the last digit in the total. Since the 6 in 1.756 is
uncertain, this makes the 0 in 1.7604 also uncertain, and the 4 following it a meaningless
number. The proper way to write the total width of the bench is with just one uncertain
digit, 1.760 m.
Now imagine you have a graduated cylinder containing 12.00 mL of water.
You carefully lower a glass marble into the graduated cylinder, and observe that the water
level rises to 14.20 mL. What is the volume of the glass marble? To find out, you subtract
the two measurements:
14.20 mL
–12.00 mL
2.20 mL
Notice that when the two measurements are subtracted, you lose a significant digit
in this particular situation. What if the object added to the water was a small lead pellet
and the volume increased from 12.00 mL to 12.20 mL? The volume of the pellet would
be 0.20 mL. This measurement has only two significant digits. When measurements are
subtracted, there is often a loss of precision.
Here is a common sense rule for adding or subtracting measurements:
When adding or subtracting measurements, the sum or difference will have as many
digits after the decimal point as the single measurement with the least number of
digits after the decimal point.
© Edvantage Interactive 2012 ISBN 978-0-9864778-3-6 Chapter 1 Skills, Methods, and the Nature of Physics 13