A metrological approach to quantities that are counted and the unit one

Abstract

There has long been debate over how to treat dimensionless quantities, or quantities with the unit one, within the International System of Units (SI). These arguments have been brought into sharper focus because of the increasing application of metrological principles in areas such as chemistry, biology and nanoscience where counting measurements are common. This has caused debates about how the SI should address counting quantities and the unit one (symbol 1). This article reviews the types of quantities with the unit one, how these quantities may be expressed together with their uncertainty and how this relates to counting. The qualities of counting quantities are explored in more detail and the range of possibilities for dealing with the unit one for counting are discussed. It is proposed that the SI should allow only the unit one for counting, but that downstream of the SI there may well be benefits from standardising the use of more descriptive, technical area specific ‘units’ for expressing the results of counting. As with all measurement it is essential that a full description, in words, of the counting quantity being expressed accompanies the measurement result.

Unit one is intrusive

“…In 2021, Brown reviewed the situation with counted quantities and unit one, expanding on the issues of traceability and realisation of units [ 34 ].…”

“…For dimensionless ratios, we know that the numerator and denominator will have meaningful traceability if they are considered separately. For counts, we know that some definition for the identification of the entities or events counted must exist, ideally in a standard that is ‘downstream’ [ 34 ] of the SI brochure. Section 4: acknowledge the role of ‘downstream’ standards for other units and remove the implication that any units not listed in the brochure are ‘unacceptable’ (cf.…”

“…For dimensionless ratios, we know that the numerator and denominator will have meaningful traceability if they are considered separately. For counts, we know that some definition for the identification of the entities or events counted must exist, ideally in a standard that is ‘downstream’ [ 34 ] of the SI brochure.…”

What does the pixel measure?

“…In practice, we cannot afford the mistake of equating bits to bytes or neutrons to pixels, so we often indicate units of counting. Reconciling this practice with SI guidance on the use of unit symbols and names remains a topic of ongoing discussion [17][18][19][20][21].…”

Redefinition of the Mole in the Revised International System of Units and the Ongoing Importance of Metrology for Accurate Chemical Measurements

“…The definitions of the base units, including the mole, are now formulated in a way that allows future advances in technology to be turned directly into improvements in the accuracy of measurements, also allowing more direct access to the benefits of the new definitions for end users. The new base unit definitions provide ongoing flexibility for our measurement system so that it is ready to accommodate all future technological and scientific advances, some of which may well affect chemical measurement, for instance routine single molecule detection and identification …”