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Innovation for Our Energy Future 

Rounding and Significant 

Figures 

Laboratory Analytical Procedure (LAP) 

Issue Date: 07/17/2005 

B. Michener, C. Scarlata, and B. Hames 

Technical Report 

NREL/TP-510-42626 

January 2008 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337

Technical Report 

NREL/TP-510-42626 

January 2008 

Rounding and Significant 

Figures 

Laboratory Analytical Procedure (LAP) 

Issue Date: 07/17/2005 

B. Michener, C. Scarlata, and B. Hames 
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Procedure Title: Rounding and Significant Figures 

Laboratory Analytical Procedure 

1. Introduction 

1.1 This procedure describes the rules for rounding numbers for the reporting of analytical 

data.

2. Scope 

2.1 This method describes the application of significant figures for the proper reporting of 

analytical data 

3. Terminology 

3.1 Significant Figures: The number of significant figures in a measured quantity is the 

number of digits that are known accurately, plus one that is in doubt. Zeroes that 

appear to the left of the first nonzero digit are placeholders and are not considered 

significant. Zeros located to the right of the first digit may be considered significant. 

3.2 Analytical Data: Data that represent the measured concentration or value of analytes in 

a sample aliquot. Sample aliquots include samples, method blanks, calibration 

verification standard (CVS) and quality assurance samples (QA samples, e.g. NIST 

standards). 

3.3 Sample Data. Data that represents the measured concentration of analytes in a sample. 

3.4 Method Blank Data: Data that represent the measured concentration of analytes 

measured in a all reagents without the addition of a sample. 

3.5 Quality control (QC) Data: Data that represent the measured concentration of target 

analytes that are elements of QA and CVS samples. 

3.6 Quality Assurance Data: Data the represent the known values in a standard refernce 

material 

3.6 Accuracy Data: Data that represent the percent recovery determined from QC data. 

3.7 Precision Data: Data that represent the relative percent difference or relative standard 

deviation calculated from accuracy data. 

3.8 Calibration Range: The range of a method is defined as the lower and upper 

concentrations for which the analytical method has adequate accuracy, precision and 

linearity. 

4. Significance and Use 

4.1 It is the responsibility of each analyst recording analytical data to comply with each of 

these rules for significant figures and rounding. 

4.2 It is the responsibility of each supervisor, data reviewer, or QA representative to ensure 

that these rules are properly applied in the treatment of analytical data. 

5. Interferences 

5.1 Not applicable 

 1
6. Apparatus 

6.1 Not applicable 

7. Reagents and materials 

7.1 Not applicable 

8. ES&H Considerations and Hazards 

8.1 Not applicable 

9. Procedure 

9.1 All calculations should be completed prior to any rounding to avoid introducing 

additional error into the analytical result. 

9.2 Data entry into calculators or computers should include all of the available digits from 

the analytical instrument generating the data. Some instrument outputs contain an 

excessive numbers of digits. In these cases data entry should be at least 5 digits (if 

available) to prevent error due to successive rounding. 

9.3 The calibration range must be reported using the same rounding and significant figures 

rules as the associated sample data. 

9.4 Data below the calibration range prior to rounding should be reported as <(the lower 

end of the calibration range). Example: If your calibration range is 500 - 100 ppm, and 

your instrument reports a value below 100 ppm, the data should be reported as “<100 

ppm”.] 

9.5 Results from the measurement of Method Blank samples results should be treated as 

analytical data and reported with the same number of significant figures as the 

associated sample data. 

10. Rounding Rules 

10.1 When the digit following the last the last significant digit is less than 5, the number 

remains unchanged (round down.) 

Example: 1.63 is rounded to 1.6 

10.2 When the digit following the last the last significant digit is greater than 5, the digit to 

be retained is increased by 1. 

Example: 2.6 is rounded to 2.7 

10.3 When the digit following the last the last significant digit equals 5, the number is 

rounded off to the nearest even number. 

Example: 3.85 is rounded to 3.8, 4.55 is rounded to 4.6 

Note: Some automated systems such as spreadsheets, calculators and data management 

software always round up a five. 

10.4 When calculations are complete and two or more figures are to the right of the last the 

last significant digit, rounding begins at the least certain digit and continues until the 

correct number of digits remains. 

Example: Rounding to two significant figures: 

2.4501 is viewed as 2.4(501) and is rounded to 2.5 

2.5499 is viewed as 2.5(499) and is rounded to 2.5 

 2
10.1 Significant Figures 

10.1.1 The rounding rules described in Section 10 must be used to report data to the proper 

number of significant figures. This section describes how to determine the proper 

number of significant figures. 

10.1.2 The number of significant figures in a measured quantity is the number of digits that 

are known accurately, plus one that is in doubt. Zeroes that appear to the left of the 

first nonzero digit are placeholders and are not considered significant. Zeros located 

to the right of the first digit may be considered significant. The concept of 

significant digits applies only to measured quantities and to results calculated from 

measured quantities. It is never applied to exact numbers or definitions. 

Example: the answer has three significant 

figures because the conversion factor is a definition. 

÷ = min263.0minsec/60sec8.15

10.1.3 A final result should never contain any more significant digits than the least precise 

data used to calculate it. 

11. Calculations 

11.1 To report or calculate the relative percent difference (RPD) between two samples, use 

the following calculation 

RPD = 1 (X − X2)

X mean

⎛

⎝ ⎜ ⎞⎠ ⎟ × 100

Where: 

X1 and X2 = measured values 

Xmean = the mean of X1 and X2 

11.2 To report or calculate the root mean square deviation (RMS deviation) or the standard 

deviation (std. dev.) of the samples, use the following calculations. 

First find the root mean square (RMS), of the sample using 

RMS = x m = mean = 

x

1

n

∑

 n 

⎛ 

⎝ 

⎜ 

⎜ 

⎜ 

⎜ ⎜ 

⎞ 

⎠ 

⎟ 

⎟ 

⎟ 

⎟ ⎟ 

2

Then find the root mean square deviation, or standard deviation, using 

RMSdeviation = σ = stdev =

xi − x ( ) m

2

1

n

∑

n

 3
Where: 

xm=the root mean square of all x values in the set 

n=number of samples in set 

xi=a measured value from the set 

12. Report Format 

12.1 Not applicable 

13. Precision and Bias 

13.1 Not applicable 

14. Quality Control 

14.1 Not applicable 

15. Appendices 

15.1 Not applicable 

16. References 

16.1 The Chemical Technicians Ready Reference Handbook, 4th Ed. , Gershon J. Shugar 

and Jack T. Ballinger, 1996, New York, New York, McGraw-Hill, Inc. 

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