Rules for Significant Figures:

 

Significant figures are very important in helping determine how to report a number. The following table provides some general guidelines in assessing how many figures to present:

 

     If you know the number to:             Report this many figures:

 

1 part per 10                                       1

1 part per 100                                     2

1 part per 10 00                                   3

1 part per 10 000                                 4

1 part per 10 0 000                              5

1 part per 1 000 000                            6

etc.                                                     etc.

 

Rules in determining the number of significant figures in a number:

 

1.     All digits are significant except zeros at the beginning of the number, and possibly terminal zeros.

 

2.     Terminal zeros ending at the right of the decimal point are significant.

 

3.     Terminal zeros in a number without an explicit decimal point may or may not be significant.

 

The third rule may be cause for confusion.  Consider these examples:

 

0.0025              2 Significant Figures

252                   3 Significant Figures

250                   2 or 3 Significant Figures

 

To avoid ambiguity, engineers often use scientific notation:

     2.5 x 10-3

     2.52 x 102

     2.50 x 102          (3 significant figures)

 

Significant Figures in Calculations:

 

1.  When multiplying or dividing measured quantities, round the answer to as many significant figures in the answer as there are in the measurement with the least number of significant figures.

 

2.     When adding or subtracting measured quantities, round the answer to the same number of decimal places as there are in the measurement with the least number of decimal places.

 

Examples:

     5.0  x 10.624     = 53.120   à                   Answer: 53

 

     5.0  + 10.624    = 15.624   à                   Answer: 15.6

 

 

Significant Figures and Exact Numbers:

 

Conversion factors should be considered exact numbers. In other words, significant digits depend on the converted number not the conversion factor.

 

1 inch = 2.54 centimeters           1.00000000+ = 2.5400000000+

where + indicates an infinite number of zeros. Generally, the + is understood and therefore not written.

 

 

Reporting Statistical Results and Probability Calculations:

 

As a general rule, statistics for a measured value (length, time, weight) should be reported to one additional digit beyond the level of precision. For example, if you measure to the nearest 1 mm, report the average to the nearest 0.1 mm.

 

In the case of probabilities and proportions (which are unit-less), solutions should be reported to appropriately reflect the analysis. For instance, if you sample 80 parts and compute a proportion defective, you might report your results to two or three places (14% or 13.8%).

 

In calculating the probability of a defect, we typically report probabilities to five or six places such as 0.00135. One reason is that to compute defects per million, these probabilities are multiplied by 1 million. (Similar rules often apply to reporting reliability figures.)