Editing Roman numerals (section)

===Fractions===
[[File:Vecchi 003.jpg|thumb|left|upright=0.7|A {{lang|la|[[triens]]}} coin ({{frac|1|3}} or {{frac|4|12}} of an {{lang|la|as}}). Note the four dots ('''····''') indicating its value.]]
[[File:Semisse.jpg|thumb|right|upright=0.9|A {{lang|la|[[semis]]}} coin ({{frac|1|2}} or {{frac|6|12}} of an {{lang|la|as}}). Note the {{rn|S}} indicating its value.]]

The base "Roman fraction" is {{rn|S}}, indicating {{frac|1|2}}. The use of {{rn|S}} (as in {{rn|VIIS}} to indicate 7{{frac|1|2}}) is attested in some ancient inscriptions<ref>{{Cite web |title=RIB 2208. Distance Slab of the Sixth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2196 |access-date=11 November 2020 |website=Roman Inscriptions in Britain}}</ref> and in the now rare apothecaries' system (usually in the form {{rn|SS}}):<ref name="Bachenheimer" /> but while Roman numerals for [[Integers|whole numbers]] are essentially [[decimal]], {{rn|S}} does not correspond to {{frac|5|10}}, as one might expect, but {{frac|6|12}}.

The Romans used a [[duodecimal]] rather than a decimal system for [[rational number|fractions]], as the [[divisibility]] of twelve {{nowrap|1= (12 = 2<sup>2</sup> × 3)}} makes it easier to handle the common [[Fraction (mathematics)|fractions]] of {{frac|1|3}} and {{frac|1|4}} than does a system based on ten {{nowrap|1= (10 = 2 × 5)}}. Notation for fractions other than {{frac|1|2}} is mainly found on surviving [[Roman coin]]s, many of which had values that were duodecimal fractions of the unit {{lang|la|[[As (coin)|as]]}}. Fractions less than {{frac|1|2}} are indicated by a dot ('''·''') for each {{lang|la|uncia}} "twelfth", the source of the English words ''inch'' and ''ounce''; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is {{rn|S}} for {{lang|la|semis}} "half". ''Uncia'' dots were added to {{rn|S}} for fractions from seven to eleven twelfths, just as tallies were added to {{rn|V}} for whole numbers from six to nine.<ref>{{Cite journal |last1=Maher |first1=David W. |last2=Makowski |first2=John F. |date=2011 |title=Literary Evidence for Roman Arithmetic with Fractions |url=http://dmaher.org/Publications/romanarithmetic.pdf |journal=Classical Philology |volume=96 |issue=4 |pages=376–399 |doi=10.1086/449557 |s2cid=15162149 |archive-url=https://web.archive.org/web/20130827220707/http://dmaher.org/Publications/romanarithmetic.pdf |archive-date=27 August 2013}}</ref> The arrangement of the dots was variable and not necessarily [[Linearity|linear]]. Five dots arranged like ('''⁙''') (as on the face of a [[dice|die]]) are known as a [[quincunx]], from the name of the Roman fraction/coin. The Latin words {{lang|la|sextans}} and {{lang|la|quadrans}} are the source of the English words ''[[sextant]]'' and ''[[Quadrant (plane geometry)|quadrant]]''.

Each fraction from {{frac|1|12}} to {{frac|12|12}} had a name in Roman times; these corresponded to the names of the related coins:

{| class="wikitable"
! Fraction
! Roman numeral
! Name (nominative and genitive singular)
! Meaning
|-
| {{frac|1|12}}
| '''·'''
| {{lang|la|[[Uncia (coin)|Uncia]], unciae}}
| "Ounce"
|-
| {{frac|2|12}} = {{frac|1|6}}
| '''··''' or ''':'''
| {{lang|la|[[Sextans (coin)|Sextans]], sextantis}}
| "Sixth"
|-
| {{frac|3|12}} = {{frac|1|4}}
| '''···''' or '''∴'''
| {{lang|la|[[Quadrans]], quadrantis}}
| "Quarter"
|-
| {{frac|4|12}} = {{frac|1|3}}
| '''····''' or '''∷'''
| {{lang|la|[[Triens]], trientis}}
| "Third"
|-
| {{frac|5|12}}
| '''·····''' or '''⁙'''
| {{lang|la|[[Quincunx (Roman coin)|Quincunx]], quincuncis}}
| "Five-ounce" ({{lang|la|quinque unciae}} → {{lang|la|quincunx}})
|-
| {{frac|6|12}} = {{frac|1|2}}
| {{rn|S}}
| {{lang|la|[[Semis]], semissis}}
| "Half"
|-
| {{frac|7|12}}
| {{rn|S}}'''·'''
| {{lang|la|Septunx, septuncis}}
| "Seven-ounce" ({{lang|la|septem unciae}} → {{lang|la|septunx}})
|-
| {{frac|8|12}} = {{frac|2|3}}
| {{rn|S}}'''··''' or {{rn|S}}''':'''
| {{lang|la|[[Bes (coin)|Bes]], bessis}}
| "Twice" (as in "twice a third")
|-
| {{frac|9|12}} = {{frac|3|4}}
| {{Rn|S}}'''···''' or {{rn|S}}'''∴'''
| {{lang|la|[[Dodrans]], dodrantis}}<br />'''or''' {{lang|la|nonuncium, nonuncii}}
| "Less a quarter" ({{lang|la|de-quadrans}} → {{lang|la|dodrans}})<br />'''or''' "ninth ounce" ({{lang|la|nona uncia}} → {{lang|la|nonuncium}})
|-
| {{frac|10|12}} = {{frac|5|6}}
| {{Rn|S}}'''····''' or {{rn|S}}'''∷'''
| {{lang|la|Dextans, dextantis}}<br />'''or''' {{lang|la|decunx, decuncis}}
| "Less a sixth" ({{lang|la|de-sextans}} → {{lang|la|dextans}})<br />'''or''' "ten ounces" ({{lang|la|decem unciae}} → {{lang|la|decunx}})
|-
| {{frac|11|12}}
| {{Rn|S}}'''·····''' or {{rn|S}}'''⁙'''
| {{lang|la|Deunx, deuncis}}
| "Less an ounce" ({{lang|la|de-uncia}} → {{lang|la|deunx}})
|-
| {{frac|12|12}} = 1
| {{rn|I}}
| {{lang|la|[[As (Roman coin)|As]], assis}}
| "Unit"
|}

Other Roman fractional notations included the following:

{| class="wikitable"
! Fraction
! Roman numeral
! Name (nominative and genitive singular)
! Meaning
|-
| {{frac|1|1728}}=12<sup>−3</sup>
| {{rn|𐆕}}
| {{lang|la|[[Siliqua]], siliquae}}
| <!-- translation needed -->
|-
| {{frac|1|288}}
| {{rn|{{Roman|1/288|fraction=yes}}}}
| {{lang|la|Scripulum, scripuli}}
| "[[Apothecaries' system|scruple]]"
|-
| {{frac|1|144}}=12<sup>−2</sup>
| {{rn|<s>Ƨ</s>}}
| {{lang|la|Dimidia sextula, dimidiae sextulae}}
| "half a sextula"
|-
| {{frac|1|72}}
| {{rn|Ƨ}}
| {{lang|la|[[Sextula]], sextulae}}
| "{{frac|6}} of an uncia"
|-
| {{frac|1|48}}
| {{rn|Ↄ}}
| {{lang|la|Sicilicus, sicilici}}
| <!-- translation needed -->
|-
| {{frac|1|36}}
| {{rn|ƧƧ}}
| {{lang|la|Binae sextulae, binarum sextularum}}<br>(Exceptionally, these are plural forms.)
| "two sextulas" ({{lang|la|[[duella]], duellae}})
|-
| {{frac|1|24}}
| {{rn|Σ}} or {{rn|𐆒}} or {{rn|Є}}
| {{lang|la|[[Semuncia]], semunciae}}
| "{{frac|2}} uncia" ({{lang|la|semi-}} + {{lang|la|uncia}})
|-
| {{frac|1|8}}
| {{rn|Σ}}'''·''' or {{rn|𐆒}}'''·''' or {{rn|Є}}'''·'''
| {{lang|la|Sescuncia, sescunciae}}
| "{{frac|1|1|2}} uncias" ({{lang|la|[[Numeral prefix|sesqui]]-}} + {{lang|la|uncia}})
|}

Fractions could also be indicated with a slash through the last letter in a numeral (e.g. {{rn|Ɨ}}), which subtracted the number by an amount less than one (usually {{frac|1|2}}).<ref name=cappelli/>