GeoE 308 Hydrogeology Spring, 1998
Notes on significant figures and dimensional analysis
Significant figure rules (see p. 22-23 of Fetter):
# sig. figs
17
17.00
0.017
0.0170
2
4
2
3
NOTE: difference between “measured” vs.
“hypothetical” quantity. If I ask you, “how many feet in 1 mile?” The correct answer is 5280, not 5000. This is because it is
1700 2, 3 or 4
1.7 x 10
3
2
1.700 x 10
3
4 understood that the mile is a hypothetically exact mile, not a measured mile, and so the sig-fig rules no longer apply. On the other hand, if I measure the distance between two points on a map as 1.6 miles and ask the same question, the answer is (1.6 miles x 5280 ft/mile) = 8448, rounded to 8400 feet .

For multiplication/division, round answer off to the # of sig. figs. in the least precise measured variable.
Example: (20.5 x 1200)/3 = 8,000 (or 8 x 10
3
, or 8 E+03)

For addition/subtraction, the answer should not have any sig. digits to the right of the last sig. digit of any of the measured variables.
Example: 17 + 2.35 + 0.0725 = 19 (not 19.4225)

Carry all sig. figs through a multi-step calculation, and then round off at the end.
For this class, it is OK to report your answer to 1 extra significant figure . This avoids unnecessary round-off errors.
Dimensional analysis (see p. 22-23 of Fetter)
Many problems can be solved merely by setting up proper conversion ratios, and then making sure your units cancel. Common abbreviations: L = length, M = mass, T = time.
EXAMPLE: If the flow in an irrigation ditch is 12 liter/minute, how many acre-feet of irrigation is possible in one year?
First, do a dimensional analysis to see if the two units are compatible: liters/minute = L 3 /T acre-feet/year = L
2 
L/T = L
3
/T ... ok
12 L 0 0353 x
.
min L ft
3 x
= 5.1 acre
 ft/year
1 acre
43560 ft
2 x
60 min hr x
24 hr day x
365 day year

 year