Use of Significant Figures
For homework assignments in Geo 346C, I will deduct points for incorrect use of
significant figures. A number of students have asked me about this, so here are the
guidelines that I will follow when grading your homework assignments.
Follow the rules for significant figures given in the textbook (Applied Hydrogeology,
C.W. Fetter) on page 19.
The one instance that I differ from “significant figures rules” is if the input data warrant
the use of only one significant figure in your final answer, I will accept two significant
figures. If you use three or more significant figures, then the input data must justify it.
It is obvious that both 12.0 and 0.0120 each have three significant figures, but how many
significant figures does 120 have? Three or two? In keeping with the textbook, we will
assume that the 0 in 120 is significant and so we will assume that 120 has three
significant figures.
To avoid ambiguity in the answers that you provide to me in your homework
assignments, I recommend that you use scientific notation. For example, write 120 as
1.2 × 102 if you mean to communicate that it has two significant figures or write it as
1.20 × 102 if you mean to communicate that it has three significant figures.
The number of significant figures for conversion factors and constants will almost always
exceed the number of significant figures of the given input data. Sometimes we round
conversion factors for ease of use. For example, during class we may use 1 g/cm3 for the
density of water which is a nice round number for rough calculations. If we were being
very precise, the density of water at 20°C is about 0.99829 g/cm3. In most cases using
the more precise value will give the exact same result as using the rounded value of 1
g/cm3, but it is important to be aware of the rounding done to conversion factors and
constants. There will be times when it is appropriate to use very precise values for
conversion factors and constants.
When solving a problem that requires multiple calculations (multiple steps), I recommend
that you not round numbers determined in the intermediate steps. Carry extra digits
through the intermediate steps and then round your final answer to the appropriate
number of significant figures. This will help you to avoid rounding errors.