The Decimal Deception
How Significant Figures may produce
unacceptable evaluations.

Article written by Harlan Mott, Information Technology Developer, Analytical Products Group

Complete Article from Edition 7 APG eNewsletter

How does it make you feel to know that you may have receive an unacceptable evaluation when your data could have been acceptable? At APG we receive data returns every study with results not in three significant figures. These results are required to be evaluated as received against three significant figure limits. What this means is that by not reporting three significant figures you are making it more difficult to receive an acceptable evaluation and may even cause the analyte to be unacceptable. Here are some examples of how this oversight can affect your evaluation.

Assume you tested for iron and the actual result was 3473.92. If you reported your result to APG as 3474, four significant figures, and the upper limit on iron was 3470. With a reported result of 3474, the evaluation would be "not acceptable" as you are above the upper limit. By reporting your data as three significant figures, 3473.92 would be reported as 3470 and your result would be acceptable.

Try It For Yourself...   Calculate Three Significant Figures   Actual Number:  3 Significant Figures:

Iron with actual result of 3473.92

Lower Limit	Reported Result	Upper Limit	Evaluation
3230	3474 (4 sig. fig.)	3470	Not Acceptable
3230	3470 (3 sig. fig.)	3470	Acceptable

The analytes with smaller values are those that most frequently are reported in more than three significant figures and the differences are often more dramatic. If you analyze Total Residual Chlorine and receive an actual result of 2.24569 and report in three decimal places, you would report 2.246. If the lower limit is 2.25 with a result of 2.246, you would be evaluated as "unacceptable" because you are below the lower limit. If the 2.24569 had been reported as three significant figures and not three decimal places the result would have been 2.25 and you would have passed total residual chlorine.

Total Residual Chlorine with actual result of 2.24569

Lower Limit	Reported Result	Upper Limit	Evaluation
2.25	2.246 (4 sig. fig.)	3.02	Not Acceptable
2.25	2.25 (3 sig. fig.)	3.02	Acceptable

I hope this clarifies why you should use three significant figures when reporting PT results. It does not help much if you do not understand how to convert your numbers into three significant figures so, lets look at how to determine which figures are significant.

Significant Figures Rules
Rule #1
Non-zero integers are always significant; or any number besides zero is always significant.
2.234 has four significant figures
3475 has four significant figures

Rule #2
Zero's bound on both sides with non-zero integers are always significant.
2.003 has four significant figures
1009 has four significant figures

Rule #3
Zero's not bound on the left side by non-zero integers are never significant. These zeros are placeholders.
0.024 has two significant figures
0.0091 has two significant figure

Rule #4
Trailing zeros are the only exception, in that they are sometimes significant. It is significant if the zero would be displayed in scientific notation. It is not significant if it would be omitted in scientific notation. For the purpose of PT testing determing the signficance of trailing zero's will not affect your evaluation. Both 450.0 and 450 will evaluate the same so this rule is not important for reporting your PT results. You should follow rules #1 - #3 when testing PT data.
450.0 or 4.50x10e2 has three significant figures
450 or 4.5x10e2 has two significant figures

APG is always working for you
I have developed an online resource to convert numbers to three significant figures.

Sincerely,
Harlan Mott III
IT Developer
MCP+SB,MCSD,MCT