NATA


Significant Figures and Rounding of Data

Clause 5.10.1 of Australian Standard AS ISO/IEC 17025 ‘General requirements for the competence of testing and calibration laboratories’ notes that ‘the results of each test, calibration, or series of tests or calibrations carried out by the laboratory shall be reported accurately, clearly, unambiguously and objectively, and in accordance with any specific instructions in the test or calibration methods’.  However, the Standard does not specifically mention the use of significant figures and the procedures to be followed for rounding, although Clause 5.4.6.2 refers to it obliquely, noting that testing laboratories ‘shall ensure that the form of reporting of the result does not give a wrong impression of the uncertainty’

The number of significant figures is meant to reflect the accuracy of a test result; consequently results on a test report that contain more significant figures by inference would be considered more accurate.   Unfortunately this has led to some laboratories attempting to gain commercial advantage by reporting a greater number of significant figures than appropriate. 

The number of significant figures used should be based on the calculated or estimated measurement uncertainty for the test method.  As a general guideline, the results obtained from the majority of chemical tests are reported to two significant figures; however there are exceptions, depending on the test equipment and calibration procedures. 

Where the result is less than the method limit of reporting, only one significant figure should be used.  In addition a result should not have an implied accuracy greater than the original values from which it was derived (i.e. If the input values are stated to two significant figures only, then the reported value should not exceed a maximum of two significant figures).

Australian Standard AS 2706 ‘Numerical values - Rounding and interpretation of limiting values’ describes the procedures to be followed in determining the number of significant figures and the standard practice for rounding.  The number of significant figures is defined as the number of figures counted to the right from the leftmost non-zero figure inclusive.  Rounding is typically done to the nearest unit in the last place retained, although sometimes two and five unit rounding is conducted.

Simplistically, rules for the rounding of test results are as follows:

If the figure in the place following the retained figure is less than 5, then retain the existing figure, i.e. round down (e.g. 5.34 rounds to 5.3).

  • If the figure in the place following the last retained figure is greater than 5, or 5 followed by any other number, then add 1 to the last retained figure, i.e. round up (e.g. 5.36 rounds to 5.4; 5.551 rounds to 5.6).
  • If the figure in the place following the last retained figure is equal to 5 followed by only zeros, then choose the even round value (e.g. 5.35 rounds to 5.4; 5.45 rounds to 5.4), with zero regarded as an even number.
  • Rounding of the last retained figure should be made in one step by applying the rounding rule to the most complete value obtained (e.g. 5.2454 rounded to three significant figures is 5.25 not 5.24).

When data is used in calculations it is especially important that rounding is only conducted when the final test result is obtained, otherwise errors can accumulate.  In addition, rounding practices inherent in computer programmes and calculators vary so these should be checked.

Further detail on the procedures to be employed should be obtained from AS 2706, especially when rounding is carried out to two or five units.

Frank Fleer
Chair, Chemical Testing Accreditation Advisory Committee

(Frank Fleer is Principal with Golders Associates. Golder Associates hold accreditation with NATA in the fields of Chemical Testing and Construction Materials Testing.  Frank is also the Chair of NATA’s Chemical Testing Accreditation Advisory Committee and has been Member of the Committee since 2009, providing technical advice in the area of air testing).

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