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Roman numerals are expressed by letters of the alphabet:
I=1; V=5; X=10; L=50; C=100; D=500; M=1000
There are four basic principles for reading and writing Roman numerals:
- A letter repeats its value that many times (XXX = 30, CC = 200, etc.). A letter can only be repeated three times.
- If one or more letters are placed after another letter of greater value, add that amount.
VI = 6 (5 + 1 = 6)
LXX = 70 (50 + 10 + 10 = 70)
MCC = 1200 (1000 + 100 + 100 = 1200)
- If a letter is placed before another letter of greater value, subtract that amount.
IV = 4 (5 – 1 = 4)
XC = 90 (100 – 10 = 90)
CM = 900 (1000 – 100 = 900)
Several rules apply for subtracting amounts from Roman numerals:
- Only subtract powers of ten (I, X, or C, but not V or L)
For 95, do NOT write VC (100 – 5).
DO write XCV (XC + V or 90 + 5)
- Only subtract one number from another.
For 13, do NOT write IIXV (15 – 1 – 1).
DO write XIII (X + I + I + I or 10 + 3)
- Do not subtract a number from one that is more than 10 times greater (that is, you can subtract 1 from 10 [IX] but not 1 from 20—there is no such number as IXX.)
For 99, do NOT write IC (C – I or 100 – 1).
DO write XCIX (XC + IX or 90 + 9)
- A bar placed on top of a letter or string of letters increases the numeral’s value by 1,000 times.
XV = 15; = 15,000
Despite the fall of the Roman Empire millennia ago and despite the ubiquitous, worldwide use of Arabic numerals (1, 2, 3, etc.), Roman numerals still pop up regularly in modern society. We see them in the names of popes and monarchs and august events like the Olympics, the Super Bowl, and WrestleMania (who can forget the drama and excitement of WrestleMania III?). They sometimes appear on the pillars of docks and the outside of the hulls of ships, to indicate how high the water is, and they’re often engraved on the cornerstones of buildings, to indicate the date they were laid. And for some odd reason, Roman numerals are used to designate the year of production on films.
A Very Brief History of Roman Numerals
Several hypotheses exist as to the origin of Roman numerals. The common thread through all of them is that the numerals were developed primarily as a counting system for commerce, with the most popular theory being that they began as notches on tally sticks. A single notch represented “one.” Every fifth notch was double cut to form a “V” shape and every tenth notch was double crossed to form an “X.” The Romans later transferred this tally system to writing and designated Roman letters to certain values: I → 1; V → 5; X → 10, etc.
Another theory posits that the numerals originated from finger counting. Each finger represented a numeral. The numeral “V” (five) represented a hand held upright with the fingers and thumb apart. The numeral “X” (ten) represented both hands held upright and the two thumbs crossing each other.
A defining and extremely limiting trait of the Roman numeral system is that it lacks a character to designate the number 0. The system also has no way to represent negative or decimal numbers. This all goes back to the fact that Roman numerals were developed primarily to count and keep track of things for commerce. Consequently, higher-level math was and is pretty much impossible with this system.
Even after the decline of the Roman Empire, their numerals continued to be used throughout Europe, up through the Middle Ages. It wasn’t until the 14th century that Hindu-Arabic numerals replaced Roman numerals en masse. Even after the rise of the former, the Roman system continued on as a sort of antiquated shout out to things old and classic.