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The first usage of the symbols began showing up between 900 and 800 B.C.
The origins of the system are obscure and there are several theories, all just suppositions.
The Roman numerals, in particular, are directly derived from the Etruscan number symbols: "𐌠", "𐌡", "𐌢" and "𐌣".
Roman Numerals were first used for counting and trade, and then they started to appear on calendars and sundials.

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(Image credit: WarpFlyght/Creative Commons)

Roman numerals originated, as the name might suggest, in ancient Rome. There are seven basic symbols: I, V, X, L, C, D and M. The first usage of the symbols began showing up between 900 and 800 B.C.

The numerals developed out of a need for a common method of counting, essential to communications and trade. Counting on one's fingers got out of hand, so to speak, when you reached 10. So, a counting system was devised based on a person's hand.

Meaning of Roman numerals

A single line, or "I," referred to one unit or finger; the "V" represented five fingers, specifically, the V-shape made by the thumb and forefinger. "X" equaled two hands. (See how an X could be two Vs touching at their points?)

Larger Roman numerals developed from other symbols.

M = 1,000 - Originally, the Greek letter phi - Φ - represented this value. It was sometimes represented as a C, I and backwards C, like this: CIƆ - which sort of looks like an M. It's only a coincidence that mille is the Latin word for a thousand.

D = 500 - The symbol for this number was originally IƆ - half of CIƆ.

C = 100 - The original symbol was probably theta - Θ - and later became a C. It only coincidentally also stands for centum, the Latin word for a hundred.

L = 50 - This value was originally represented by a superimposed V and I, or by the letter psi - Ψ - which flattened out to look like an inverted T, and then eventually came to resemble an L.

How to read Roman numerals

Numbers are formed by combining various letters and finding the sum of those values. The numerals are placed from left to right, and the order of the numerals determines whether you add or subtract the values. If one or more letters are placed after a letter of greater value, you add. If a letter is placed before a letter of greater value, you subtract. For example, VI = 6 because V is higher than I. But IV = 4 because I is lower than V.

(Image credit: Michaela Stejskalova Shutterstock)

There are a number of other rules related to Roman numerals. For example, do not use the same symbol more than three times in a row. When it comes to subtracting amounts, only powers of 10 are subtracted, like I, X, or C, but not V or L. For example, 95 is not VC. 95 is XCV. XC equals 100 minus 10, or 90, so XC plus V, or 90 plus 5, equals 95.

Also, only one number can be subtracted from another. For example, 13 is not IIXV. It's easy to see how the reasoning would be: 15 minus 1 minus 1. But following the rule, it instead is XIII, or 10 plus 3.

You also cannot subtract a number from one that is more than 10 times greater. You can subtract 1 from 10 (IX) but you cannot subtract 1 from 100; there is no such number as IC. You would instead write XCIX (XC + IX, or 90+9). For larger numbers in the thousands, a bar placed on top of the letter or string of letters multiplies the numeral's value by 1,000: .

Disadvantages of using Roman numerals

Roman numerals are not without flaws. For example, there is no symbol for zero, and there is no way to calculate fractions. This hindered the ability to develop a universally understood, sophisticated math system, and made trading more difficult. Eventually, Roman numerals gave way to the more versatile Arabic or Hindu numeral system, where numbers are read as a single number in sequence, like 435 as four hundred thirty-five.

As the Roman Empire collapsed a thousand years later, Christianity (ironically one of Rome's earliest targets for persecution), continued to use the culture's number system.

Today, Roman numerals appear in building cornerstones and movie credits and titles. They are also used in names of monarchs, popes, ships and sporting events, like the Olympics and the Super Bowl.

Roman numerals are used in astronomy to designate moons and in chemistry to denote groups of the Periodic Table. They can be seen in tables of contents and in manuscript outlines, as upper- and lower-case Roman numerals break information into an easily organized structure. Music theory employs Roman numerals in notation symbols.

These uses are more due to aesthetic reasons than functional purposes. Cosmetically, Roman numerals convey a sense of history and timelessness, which is especially true in clocks and watches.
Related:

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Elaine J. Hom - Live Science Contributor

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Roman Numerals: Conversion, Meaning & Origins

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Roman numerals originated, as the name might suggest, in ancient Rome. There are seven basic symbols: I, V, X, L, C, D and M. The first usage of the symbols began showing up between 900 and 800 B.C. The numerals developed out of a need for a common method of counting, essential to communications and trade.

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Roman numerals were replaced between 1300 and 1400 AD with the end of the Roman empire, throughout most of Europe with the more effective Hindu-Arabic system still used today. A numeral is any symbol used to represent a number.
Even if the Roman numerals were replaced by the Hindu-Arabic the Roman numerals are still used today in the clocks, buildings, the SuperBowl, street numbering (in Italy) and ordinal numbers instead of 1st, 2nd, 3rd, etc.

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Science and Its Times: Understanding the Social Significance of Scientific Discovery

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Roman Numerals: Their Origins, Impact, and Limitations | Encyclopedia.com

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Roman Numerals: Their Origins, Impact, and LimitationsOverviewThe numeral system developed by the Romans was used by most Europeans for nearly 1800 years, far longer than the current Hindu-Arabic system has been in existence. Although the Roman numeral system provided for easy addition and subtraction, other arithmetic operations proved more difficult. Source for information on Roman Numerals: Their Origins, Impact, and Limitations: Science and Its Times: Understanding the Social Significance of Scientific Discovery dictionary.

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They were used for naming monarchs (kings and queens).
They were used for naming monarchs (kings and queens). Eg. King Edward VII of England and Louis XIV of France. Popes are also numbered using Roman numerals so the late Pope was John Paul II and the current Pope is Benedict XVI.

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Roman numerals are still used today and can be found in many places. They are still used in almost all cases for the copyright date on films, television programs, and videos - for example, MCMLXXXVI for 1986.