The difference between ‘amount of substance’ and ‘quantities that are a number of entities’ and implications for units of measurement
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Richard J. C. Brown
Abstract
The recent conference on “The Units, Symbols, and Terminology in the Physical Sciences in and for the Digital Era (D-UST)” highlighted the need to address the shared challenge of achieving consensus of standards and terminology for the digital age, in particular making data both human and machine readable. A key challenge is the presentation of ‘counting units’ – more properly known as units for quantities that are a number of entities. It was clear from some discussions at the conference that there is remaining confusion about the difference between ‘amount of substance’ and ‘quantities that are a number of entities’. This article attempts to delineate properly between these two different quantities, provide wider clarity on current best practice in relevant nomenclature, and explain the implications for units of measurement, expanding on comments made by the author at the conference. It also reflects on some of the latest thinking and recent progress made by the chemical metrology community in the representation of quantities that are a number of entities.
Acknowledgments
The funding of the National Measurement System by the UK Department for Science, Innovation and Technology is gratefully acknowledged.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The author states no conflict of interest.
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Research funding: UK Department for Science, Innovation and Technology: National Measurement System.
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Data availability: Not applicable.
References
1. Rab, S.; Brown, R. J. C. Nat. Rev. Phys. 2025, 7, 232; https://doi.org/10.1038/s42254-025-00819-3.Suche in Google Scholar
2. Brown, R. J. C.; Brewer, P. J. Metrologia 2020, 57, 065002; https://doi.org/10.1088/1681-7575/ab9db7.Suche in Google Scholar
3. PSDI. Units, Symbols, and Terminology in the Physical Sciences in and for the Digital Era. https://www.youtube.com/watch?v=2AmpX9OaGUQ (assessed June, 2025).Suche in Google Scholar
4. Pavese, F. Accred. Qual. Assur. 2011, 16, 161–165; https://doi.org/10.1007/s00769-010-0700-y.Suche in Google Scholar
5. Güttler, B.; Bettin, H.; Brown, R. J. C.; Davis, R. S.; Mester, Z.; Milton, M. J. T.; Pramann, A.; Rienitz, O.; Vocke, R. D.; Wielgosz, R. I. Metrologia 2019, 56, 044002; https://doi.org/10.1088/1681-7575/ab1fae.Suche in Google Scholar
6. Davis, R. S. J. Res. Natl. Inst. Stand. Technol. 2018, 123, 123021.Suche in Google Scholar
7. Levy-Leblond, J. M. Riv. Nuovo Cimento 1977, 7, 187; https://doi.org/10.1007/bf02748049.Suche in Google Scholar
8. Marquardt, R.; Meija, J.; Mester, Z.; Towns, M.; Weir, R.; Davis, R.; Stohner, J. Pure Appl. Chem. 2018, 90, 175–180; https://doi.org/10.1515/pac-2017-0106.Suche in Google Scholar
9. International Bureau of Weights and Measures. The International System of Units (SI), 9th ed.; BIPM: Sèvres, 2025.Suche in Google Scholar
10. McGlashan, M. L. Metrologia 1997, 34, 7–11; https://doi.org/10.1088/0026-1394/34/1/2.Suche in Google Scholar
11. Brown, R. J. C.; Stock, M. Metrologia 2025, 62, 013001; https://doi.org/10.1088/1681-7575/ad9479.Suche in Google Scholar
12. Brown, R. J. C.; Güttler, B.; Neyezhmakov, P.; Stock, M.; Wielgosz, R. I.; Kück, S.; Vasilatou, K. Metrology 2023, 3, 309.10.3390/metrology3030019Suche in Google Scholar
13. IUPAC. IUPAC Gold Book: Elementary Entity. https://goldbook.iupac.org/terms/view/E02033 (accessed June, 2025).Suche in Google Scholar
14. Balsamo, A. CCU-CCQM-WS/2023-13 Measuring by Counting in Length Metrology. https://www.bipm.org/en/committees/cc/ccu/wg/ccu-ccqm-ws/2023-03-28 (accessed June, 2025).Suche in Google Scholar
15. International Electrotechnical Commission. IEC 80000-13 Quantities and Units—Part 13: Information Science and Technology; IEC: Geneva, 2025.Suche in Google Scholar
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