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The seven letters are younger than the counting they record. Rome's numerals descend from the Etruscan signs for 1, 5, 10, 50 and 100, and those are usually traced in turn to notched tally sticks: a cut for each unit, a doubled cut for every fifth, a cross cut for every tenth. It is a tidy reconstruction, and widely repeated, but no ancient tally stick survives because wood rots, so it remains conjecture; tally sticks of that design were reportedly still being cut by Italian and Dalmatian shepherds in the nineteenth century. The mnemonic link between C, M and centum, mille came later. A thousand was first written Φ, or CIↃ, and D for five hundred is generally explained as half of that sign.

The system has no zero and never needed one: values are added rather than placed, so no column sits empty waiting for a marker. When medieval computists did need a zero in their Easter tables they wrote a word instead — Dionysius Exiguus used nulla in 525, and around 725 Bede used the single letter N in a table of epacts.

Subtractive notation took more than a millennium to settle. Roman inscriptions mix the conventions freely: gate 44 of the Colosseum is cut as XLIIII, and officers of Legio XVIII wrote eighteen as XIIX — the order of the Latin duodeviginti, "two from twenty" — a form that appears on the cenotaph of their senior centurion Marcus Caelius, who died in AD 9. Masons kept the older habit long afterwards: Admiralty Arch in London carries MDCCCCX for 1910 rather than MCMX. The rule taught today, with exactly six subtractive pairs and no alternatives, hardened only in the later Middle Ages and the centuries of print that followed.

Tính chất chính

• Standard notation uses exactly seven letters: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1,000.
• Only six subtractive pairs are allowed — IV, IX, XL, XC, CD and CM. A letter is never subtracted from more than ten times its own value, so IC and IM are not numerals.
• Standard notation spells every integer from 1 to 3,999 exactly one way, and 3,999 = MMMCMXCIX is as far as it reaches.
• The longest standard numeral is MMMDCCCLXXXVIII for 3,888, at fifteen letters.
• There is no symbol for zero, and none for a negative value or a decimal fraction. Fractions were handled by a separate duodecimal set, with S for one half and a dot for each twelfth.
• 1666 = MDCLXVI uses each of the seven letters exactly once, in descending order.
• An overline — the vinculum — multiplies a letter by 1,000, so V̅ = 5,000 and the largest value with a single bar is 3,999,999.
• In the apostrophus system CIↃ = 1,000, IↃↃ = 5,000, CCIↃↃ = 10,000, IↃↃↃ = 50,000 and CCCIↃↃↃ = 100,000; these forms were combined additively rather than subtractively.