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Decimal numbers and safe interpretation of clinical pathology results
  1. Michael Sinnott1,2,
  2. Robert Eley1,2,
  3. Vicki Steinle3,
  4. Mary Boyde4,
  5. Leanne Trenning1,
  6. Goce Dimeski5
  1. 1Emergency Department, Princess Alexandra Hospital, Brisbane, Australia
  2. 2Southside Clinical School, The University of Queensland School of Medicine, Woolloongabba, Queensland, Australia
  3. 3Department of Mathematics Education, University of Melbourne, Melbourne, Australia
  4. 4Department of Cardiology, Princess Alexandra Hospital, Brisbane, Australia
  5. 5Chemical Pathology, Princess Alexandra Hospital, Brisbane, Australia
  1. Correspondence to Dr Robert Eley, Southside Clinical School, The University of Queensland School of Medicine, Emergency Medicine Research Program, Princess Alexandra Hospital, Woolloongabba, QLD 4102, Australia; r.eley{at}


Objective To determine the understanding of decimal numbers by medical laboratory scientists, doctors and nurses.

Methods A Decimal Comparison Test determined the comprehension of decimals numbers. Additional questions sought the participants’ understanding of concentrations and reference ranges, and their preferences for the presentation of clinical pathology results.

Results Of the 108 participants, 40% exhibited poor comprehension of decimal numbers. One-third of the medical laboratory scientists, a quarter of doctors, and half the nurses were characterised as lacking numeracy skills. The majority of participants (60%) thought it would be safer for results to be presented as whole numbers rather than as decimals with leading zeros.

Conclusions The number of laboratory and clinical staff who show numeracy issues that could lead to misinterpretation of clinical pathology results and contribute to medical error strongly supports recommendations that pathology results should be presented as whole numbers.

  • Evidence Based Pathology
  • Diagnostics
  • Laboratory Tests

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The potential for error during interpretation of clinical pathology results that are presented as decimal numbers has been noted. White and Farrance1 stated ‘it is better to use whole numbers to avoid errors, due to possible confusion of decimal places’. More recently others have stated ‘it has generally been found that decimal point placement causes confusion’ and ‘it is easier to interpret results that are integers’.2 ,3 This presumed potential for misinterpretation prompted the ESC/ACCF/AHA/WHF Task Force for the Universal Definition of Myocardial Infarction4 ,5 to recommend a unit change so that troponin results are expressed in whole numbers. Our study tested the assumption that clinical and laboratory staff may demonstrate a misunderstanding of decimal numbers that could contribute to medical error.

Materials and methods

This was a prospective study of medical laboratory scientists, doctors and nurses working in the Emergency, Cardiology and Clinical Pathology Departments at a large metropolitan tertiary referral hospital in Australia.

The first part of the study tested the comprehension of decimals using a Decimal Comparison Test (SMART test) (figure 1). This SMART test6 contains 16 pairs of decimal numbers each of which has to be identified as greater than, smaller than or equal to its pair. A diagnostic code (table 1) is generated from the responses.

Table 1

Results of the smart test

The second part of the study used a series of questions to seek the participants’ experience in interpreting decimals, their understanding of concentrations and reference ranges, and their views on the presentation of results.


The questionnaire was completed by 23 laboratory scientists, 51 nurses, 31 doctors and three unidentified (total n=108).

Participants’ understanding of decimal numbers

Results from the SMART test (table 1) identified that 39.8% of the respondents exhibited some lack of comprehension. This was evident in 34.8% of laboratory scientists, 25.8% of doctors and 51.0% of nurses. The most common diagnostic category for nurses was ‘integrating decimals with zero’ which accounted for more than half their errors. Half the errors for the laboratory scientists and the doctors were attributable to ‘money thinking’.

Recognised problems in interpreting test results

Seventeen (16.0%) participants admitted they had difficulty in interpreting clinical pathology results which were presented as decimal numbers. Troponin was identified as one which created difficulty. However 13 of these 17 (76.5%) respondents tested as ‘Experts’. By contrast, 93.6% (59 of 63) of participants who stated that they had never experienced any difficulty were shown to have poor comprehension.

Comparison of changes in concentration

Two examples, each containing two cases of changes in concentration were presented, and for each example participants had to indicate which case had increased most relative to the other case. Half the participants were incorrect in the first example and 30% in the second (table 2).

Table 2

Ability to calculate a change in concentration

Reference ranges

Participants were asked whether values were normal or abnormal relative to reference ranges (table 3). Results suggest that as the number of decimal places exceed two, the number of false results increases.

Table 3

Ability to compare to a reference range (RR)


Sixty percent of the participants stated that their preference was for results to be presented as whole numbers. Finally, participants were asked the question ‘in a busy and noisy emergency department, which of the following presentations of Troponin results would be safer for clinicians?’ Results are presented in table 4. Of the 82 participants who expressed an opinion, 62.2% thought that the whole number (Format B) would be safer. One participant made the comment that ‘reporting small numbers always leaves the door wide open for mistakes’.

Table 4

Preference for presentation

When asked what they thought would be the preference of others, only 14% (n=15) thought that Format A would be preferable, and only five of the 23 scientists considered that format A would be a ‘safer presentation’ for Troponin results.


In a busy clinical setting, time pressure is placed on the clinicians. Not adding time pressure to the online test may have underestimated the rate of error expected in the clinical setting.


This study clearly demonstrated that a proportion of laboratory scientists and clinicians have trouble in understanding numbers with decimals which may affect their interpretation of test results. The study provides clear evidence to support recommendations that clinical pathology results should be expressed in whole numbers.1–4 We believe providing this evidence base will result in faster uptake of these recommendations.

Only 16% of the respondents recognised that they had difficulty in interpreting decimal numbers, however, over twice that proportion were shown to exhibit misunderstanding. This relatively common lack of self-awareness, or insight into one's own innumeracy, could compound the risk of errors in clinical practice and provides more reason to remove the potential problem.

Take-home messages

  • Poor comprehension of decimal numbers was illustrated by many laboratory and clinical staff.

  • Resultant misinterpretation of test results is a potential source of medical errors.

  • Whenever possible, pathology results should be presented as whole numbers.


We thank Beth Price and Eugene Gvozdenko from the University of Melbourne for their assistance with the SMART test website.



  • Correction notice This paper has been corrected since it was published online. Goce Dimeski has been added as an author of this paper.

  • Contributors MS was responsible for conception, design and interpretation. RE and VS are responsible for design, data analysis and interpretation. MB and LT are responsible for collection and assembly of data. RE wrote the first draft of the manuscript and all authors contributed to the final version.

  • Funding This work was supported by a research grant from the Queensland Emergency Medicine Research Foundation. QEMRF-EMSS-12-184

  • Competing interests None.

  • Ethics approval The University of Queensland, The University of Melbourne and Metro South Human Research Ethics Committees.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data sharing statement Unpublished data are held by the Emergency Department at the Princess Alexandra Hospital by the lead author. The authors are happy to share those data upon request.