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CEE 320 Environmental Engineering

Guidance on Significant Figures

Significant figures are important in engineering calculations because they suggest a the level of

certainty that we have in the number we are reporting. For example, it would probably be

misleading to say that a reactor should have a volume of 278.42 m3. It is probably more

appropriate to say that the volume should be 280 m

3

. Most of the material presented here isborrowed from reference Felder and Rousseau, (1986). Elementary Principles of Chemical

Processes, 2nd

Edition, Wiley.

THE SIGNIFICANT FIGURES OF A NUMBER ARE:

1. The digits from the first nonzero digit on the left to the last digit (zero or nonzero) on the

right, if there is a decimal point.

OR

2. The digits from the first nonzero digit on the left to the last nonzero digit on the right, if there

is no decimal point.

EXAMPLES: 4006 has four significant figures

12.270 has five significant figures

0.0040 has two significant figures

2300 has two significant figures2300. has four significant figures

2300.0 has five significant figures

4.00 x 10-3

has three significant figures

As noted above, the number of significant figures gives an indication of our certainty in the valuewe are reporting. For example, if we report an estimated concentration of 8.3 mg/L, then we are

saying that the true concentration is likely to be somewhere between 8.25 and 8.35 mg/L. If we

report 8.300 mg/L, then we are saying that the true concentration is likely to be somewherebetween 8.2995 and 8.3005 mg/L.

Most of us have little trouble determining how many significant figures there are in a reportednumber. Most difficulties occur when we try to add, subtract, multiply, or divide values that have

different numbers of significant figures.

When adding or subtracting numbers, compare positions of the final significant figure in eachnumber. The reported result should reflect the certainty associated with the least certain number

being added.

Examples: 12.304 + 3.16547 = 15.46947 15.469

12.304 + 3.2 = 15.504 15.5

When multiplying or dividing numbers, the reported result should have the same amount of

significant figures as the number that had the fewest significant figures.

CEE 320 Environmenta Engineering

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CEE 320 Environmental Engineering

Examples: 12.304 * 3.16547 = 38.94794288 38.948

12.304 * 3.2 = 39.3728 39

When using operations like log() and exp(), the significant figures of the result becomes ajudgement call. For this class, please follow the rules for multiplication and division for these

operations unless you have justification for doing otherwise.

When using more than one operation in the same calculation, it is usually a good idea to make

all calculations before assigning a number of significant figures.

Example involving both subtraction and division:

12.304 3.2

5.36=

9.104

5.36=1.698507463 1.7

Conversion factors: some conversion factors can be assumed to have an infinite number of

significant figures (e.g. 1000 ug/mg has an infinite number of significant figures). For lessobvious cases, assume that the number of significant figures is equal to the number reported (e.g.

3.785 liter/gallon has four significant figures).

On your exams and quizzes, points will be deducted for answers that clearly have two ore moresignificant figures than are justified (e.g. reporting 1.699 rather than 1.7 in the above example

would be more significant figures than justified while reporting 1.70 rather than 1.7 would be

okay). In most cases, reporting four or more significant figures will be considered inappropriate.

Magnitude estimates are special kinds of calculations where we usually only can justify using

one or maybe two significant figures. Examples include calculations of characteristic times or

characteristic distances. In this case, it does not matter how many significant figures go into thecalculation, you should generally not report more than one.

CEE 320 Environmenta Engineering