Editing Dimensionless quantity (section)

{{Short description|Quantity with no physical dimension}}
{{For|dimensionless physical constants|dimensionless physical constant}}
{{Use dmy dates|date=December 2022|cs1-dates=y}}
{{More citations needed|date=March 2017}}

'''Dimensionless quantities''', or quantities of dimension one,<ref>{{cite web |url=http://www.iso.org/sites/JCGM/VIM/JCGM_200e_FILES/MAIN_JCGM_200e/01_e.html#L_1_8 |title='''1.8''' (1.6) '''quantity of dimension one''' dimensionless quantity |work=International vocabulary of metrology – Basic and general concepts and associated terms (VIM) |publisher=[[International Organization for Standardization|ISO]] |date=2008 |access-date=2011-03-22}}</ref> are quantities [[implicitly defined]] in a manner that prevents their aggregation into [[unit of measurement|units of measurement]].<ref name="SI Brochure">{{cite web |url=https://www.bipm.org/en/publications/si-brochure/ |title=SI Brochure: The International System of Units, 9th Edition |publisher=[[International Bureau of Weights and Measures|BIPM]]}} ISBN 978-92-822-2272-0.</ref><ref>{{cite journal |author-last1=Mohr |author-first1=Peter J. |author-last2=Phillips |author-first2=William Daniel |author-link2=William Daniel Phillips |date=2015-06-01 |title=Dimensionless units in the SI |url=https://www.nist.gov/publications/dimensionless-units-si |journal=[[Metrologia]] |language=en |volume=52}}</ref> Typically expressed as [[ratio]]s that align with another system, these quantities do not necessitate explicitly defined [[Unit of measurement|units]]. For instance, [[alcohol by volume]] (ABV) represents a [[volumetric ratio]]; its value remains independent of the specific [[Unit of volume|units of volume]] used, such as in [[milliliter]]s per milliliter (mL/mL).

The [[1|number one]] is recognized as a dimensionless [[Base unit of measurement|base quantity]].<ref>{{Cite journal |last=Mills |first=I. M. |date=May 1995 |title=Unity as a Unit |url=https://dx.doi.org/10.1088/0026-1394/31/6/013 |journal=Metrologia |language=en |volume=31 |issue=6 |pages=537–541 |doi=10.1088/0026-1394/31/6/013 |bibcode=1995Metro..31..537M |issn=0026-1394}}</ref> [[Radian]]s serve as dimensionless units for [[Angle|angular measurements]], derived from the universal ratio of 2π times the [[radius]] of a circle being equal to its circumference.<ref>{{Cite book |last=Zebrowski |first=Ernest |url=https://books.google.com/books?id=2twRfiUwkxYC&dq=universal+ratio+of+2%CF%80+times+the+radius+of+a+circle+being+equal+to+its+circumference&pg=PR9 |title=A History of the Circle: Mathematical Reasoning and the Physical Universe |date=1999 |publisher=Rutgers University Press |isbn=978-0-8135-2898-4 |language=en}}</ref>

Dimensionless quantities play a crucial role serving as [[parameter]]s in [[differential equation]]s in various technical disciplines. In [[calculus]], concepts like the unitless ratios in [[Limits of integration|limits]] or [[derivative]]s often involve dimensionless quantities. In [[differential geometry]], the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the [[Reynolds number]] in [[fluid dynamics]],<ref>{{Cite book |last1=Cengel |first1=Yunus |url=https://books.google.com/books?id=LIZvEAAAQBAJ&dq=calculus,+concepts+like+the+unitless+ratios+in+limits+or+derivatives+often+involve+dimensionless+quantities&pg=PP1 |title=EBOOK: Fluid Mechanics Fundamentals and Applications (SI units) |last2=Cimbala |first2=John |date=2013-10-16 |publisher=McGraw Hill |isbn=978-0-07-717359-3 |language=en}}</ref> the [[fine-structure constant]] in [[quantum mechanics]],<ref>{{Cite journal |last1=Webb |first1=J. K. |last2=King |first2=J. A. |last3=Murphy |first3=M. T. |last4=Flambaum |first4=V. V. |last5=Carswell |first5=R. F. |last6=Bainbridge |first6=M. B. |date=2011-10-31 |title=Indications of a Spatial Variation of the Fine Structure Constant |url=https://link.aps.org/doi/10.1103/PhysRevLett.107.191101 |journal=Physical Review Letters |volume=107 |issue=19 |pages=191101 |doi=10.1103/PhysRevLett.107.191101|pmid=22181590 |arxiv=1008.3907 |bibcode=2011PhRvL.107s1101W }}</ref> and the [[Lorentz factor]] in [[Special relativity|relativity]].<ref>{{Cite journal |last=Einstein |first=A. |date=2005-02-23 |title=Zur Elektrodynamik bewegter Körper [AdP 17, 891 (1905)] |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.200590006 |journal=Annalen der Physik |language=en |volume=14 |issue=S1 |pages=194–224 |doi=10.1002/andp.200590006}}</ref> In [[chemistry]], [[Equation of state|state properties]] and ratios such as [[mole fraction]]s [[concentration ratio]]s are dimensionless.<ref>{{Cite journal |last1=Ghosh |first1=Soumyadeep |last2=Johns |first2=Russell T. |date=2016-09-06 |title=Dimensionless Equation of State to Predict Microemulsion Phase Behavior |url=https://pubs.acs.org/doi/10.1021/acs.langmuir.6b02666 |journal=Langmuir |language=en |volume=32 |issue=35 |pages=8969–8979 |doi=10.1021/acs.langmuir.6b02666 |pmid=27504666 |issn=0743-7463}}</ref>