page_title: Roman numerals
section_title: Fractions
hierarchical_section_title: Roman numerals / Description / Fractions
context_page_description: Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:
  The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more efficient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.
  One place they are often seen is on clock faces. For instance, on the clock of Big Ben, the hours from 1 to 12 are written as:
  I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII
  The notations IV and IX can be read as "one less than five" and "one less than ten", although there is a tradition favouring representation of "4" as "IIII" on Roman numeral clocks.
  Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs.
context_section_description: 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 = 2² × 3) 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 fraction from ​¹⁄₁₂ to ​¹²⁄₁₂ had a name in Roman times; these corresponded to the names of the related coins:
  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 fractional notations included the following:
  ​¹⁄₈ sescuncia, sescunciae (from sesqui- + uncia, i.e. ​1 ¹⁄₂ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
  ​¹⁄₂₄ semuncia, semunciae (from semi- + uncia, i.e. ​¹⁄₂ 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 (𐆒) and another resembling the Cyrillic letter Є.
  ​¹⁄₃₆ binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by a sequence of two reversed Ss (ƧƧ).
  ​¹⁄₄₈ sicilicus, sicilici, represented by a reversed C (Ɔ).
  ​¹⁄₇₂ sextula, sextulae (​¹⁄₆ of an uncia), represented by a reversed S (Ƨ).
  ​¹⁄₁₄₄ = 12⁻² dimidia sextula, dimidiae sextulae ("half a sextula"), represented by a reversed S crossed by a horizontal line (Ƨ).
  ​¹⁄₂₈₈ scripulum, scripuli (a scruple), represented by the symbol ℈.
  ​¹⁄₁₇₂₈ = 12⁻³ siliqua, siliquae, represented by a symbol resembling closing guillemets (»).
caption: A semis coin (​1⁄2 or ​6⁄12 of an as). Note the S indicating its value.
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