Roman numerals are a fascinating part of ancient history, and while they might seem simple, their use and structure are quite sophisticated. Here’s more information about Roman numerals and how they work:
Roman Numeral Rules
Roman numerals are based on a few fundamental rules for combining the letters:
- Addition: When a numeral is written after a larger numeral, the values are added together.
- Example: VIII = 5 + 3 = 8
- Subtraction: When a smaller numeral is placed before a larger numeral, the smaller numeral is subtracted from the larger one.
- Example: IV = 5 – 1 = 4
- Example: IX = 10 – 1 = 9
- Repetition: A numeral can be repeated to add up to a value, but only up to three times in a row.
- Example: III = 1 + 1 + 1 = 3
- Example: XXX = 10 + 10 + 10 = 30
- No More Than Three: No numeral appears more than three times in a row. To represent numbers like 4 or 9, subtraction is used instead.
- Example: IIII (incorrect for 4, use IV instead)
Fun Facts
- The Roman numeral system doesn’t include a symbol for zero, so Roman numerals can only represent positive whole numbers.
- The system is not positional; that is, the value of a numeral is not based on its place in a sequence, unlike the modern decimal system. This is why a numeral like IX represents 9 and XI represents 11.
Roman numerals may seem less efficient than the Arabic numeral system we use today, but they played an essential role in the development of mathematics and number systems in the ancient world.
Other subtractive forms
There are numerous historical examples of IIX being used for 8; for example, XIIX was used by officers of the XVIII Roman Legion to write their number. The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores. There are historical examples of other subtractive forms: IIIXX for 17, IIXX for 18 IIIC for 97, IIC for 98, and IC for 99. A possible explanation is that the word for 18 in Latin is duodeviginti— literally “two from twenty”— while 98 is duodecentum (two from hundred) and 99 is undecentum (one from hundred). However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.
The ROMAN() function in Microsoft Excel supports multiple subtraction modes depending on the “Form” setting. For example, the number “499” (usually CDXCIX) can be rendered as LDVLIV, XDIX, VDIV or ID. The relevant Microsoft help page offers no explanation for this function other than to describe its output as “more concise”.
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