Fractions
Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 3 × 2 × 2) makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten (10 = 2 × 5). On coins, many of which had values that were duodecimal fractions of the unit as, they used a tally-like notational system based on twelfths and halves. A dot ⟨•⟩ indicated an uncia "twelfth", the source of the English words inch and ounce; dots were repeated for fractions up to five twelfths. Six twelfths (one half) was abbreviated as the letter S for semis "half". Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.
Each of these fractions had a name, which was also the name of the corresponding coin:
| Fraction | Roman Numeral | Name (nominative and genitive) | Meaning |
|---|---|---|---|
| 1/12 | • | uncia, unciae | "ounce" |
| 2/12 = 1/6 | •• or : | sextans, sextantis | "sixth" |
| 3/12 = 1/4 | ••• or ∴ | quadrans, quadrantis | "quarter" |
| 4/12 = 1/3 | •••• or :: | triens, trientis | "third" |
| 5/12 | ••••• or :·: | quincunx, quincuncis | "five-ounce" (quinque unciae → quincunx) |
| 6/12 = 1/2 | S | semis, semissis | "half" |
| 7/12 | S• | septunx, septuncis | "seven-ounce" (septem unciae → septunx) |
| 8/12 = 2/3 | S•• or S: | bes, bessis | "twice" (as in "twice a third") |
| 9/12 = 3/4 | S••• or S:· | dodrans, dodrantis or nonuncium, nonuncii |
"less a quarter" (de-quadrans → dodrans) or "ninth ounce" (nona uncia → nonuncium) |
| 10/12 = 5/6 | S•••• or S:: | dextans, dextantis or decunx, decuncis |
"less a sixth" (de-sextans → dextans) or "ten ounces" (decem unciae → decunx) |
| 11/12 | S••••• or S:·: | deunx, deuncis | "less an ounce" (de-uncia → deunx) |
| 12/12 = 1 | I | as, assis | "unit" |
The arrangement of the dots was variable and not necessarily linear. Five dots arranged like ⟨:·:⟩ (as on the face of a die) are known as a quincunx from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.
Other Roman fractions include the following:
- 1/8 sescuncia, sescunciae (from sesqui- + uncia, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
- 1/24 semuncia, semunciae (from semi- + uncia, i.e. ½ uncia), represented by several variant glyphs deriving from the shape of the Greek letter Sigma ⟨Σ⟩, one variant resembling the pound sign ⟨£⟩ without the horizontal line(s) and another resembling the Cyrillic letter ⟨Є⟩.
- 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by ⟨ƧƧ⟩, a sequence of two reversed Ss.
- 1/48 sicilicus, sicilici, represented by ⟨Ↄ⟩, a reversed C.
- 1/72 sextula, sextulae (1/6 of an uncia), represented by ⟨Ƨ⟩, a reversed S.
- 1/144 = 12−2 dimidia sextula, dimidiae sextulae ("half a sextula"), represented by ⟨ƻ⟩, a reversed S crossed by a horizontal line.
- 1/288 scripulum, scripuli (a scruple), represented by the symbol ⟨℈⟩.
- 1/1728 = 12−3 siliqua, siliquae, represented by a symbol resembling closing guillemets ⟨»⟩.
Read more about this topic: Roman Numerals, Special Values