# Roman Numerals

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Roman numerals are similar in principle to the Greek Attic numerals. There are seven symbols in this system: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). Like the Hindu-Arabic notation, this system is a decimal system, but unlike the Hindu-Arabic system it is not a positional system.

The main way of combining these symbols to form other numbers is in an additive sort of way; just string symbols together to sum to the number you want to represent. For example, CCLXXVI is 100 + 100 + 50 + 10 + 10 + 5 + 1, or 276. Note that the symbols are always written in descending order. Another way of forming numbers is that a smaller numeral before a larger subtracts from the larger. For example, MCMXCIV is 1000 + (1000 − 100) + (100 − 10) + (5 − 1), or 1994. This second method was not used in Roman times and was only adopted in late medieval times. If you look at the numerals on an old clock, you will notice that the second method is used for 9 (IX) but not for 4 (IIII).

To represent large numbers, a bar overtop a numeral represents 1000 times the value of the numeral, and a box surrounding the number on the left, top, and right represents 100,000 times the number. So, for example, 176,328,611 could be represented as MDCCLXIIIXXVIIIDCXI.

An older way of writing large Roman numbers was that, originally, M was written as I with a ring around it (the symbol D for 500 comes from half of this original symbol for 1,000), and additional rings multiplied it by 10, so that, for example, (((I))) represented 100,000.

Roman numerals likely developed from Etruscan symbols used in central Italy. These consisted of vertical strokes indicating 1 through 4, an inverted "V" for 5, a cross (X) for 10, and combinations of these for higher figures. It may be significant that all Roman numerals below 100 consist of straight lines for easy writing or engraving.

This system suffers from the same problems inherent in systems without place value. Around the year 1000, Pope Sylvester II (Gerbert of Aurillac), a French churchman who had studied in Muslim Spain and was probably one of the greatest Christian scholars of his age, attempted to introduce the system of Arabic numbers into Europe, but his effort failed. One of the main advantages of the Arabic system was that calculations could be done on paper, but that wasn't much of an advantage in Christian Europe, which had no paper mills until 1154. In Europe, the next major appearance of Arabic numerals is in 1202, in Fibonacci's book Liber Abaci where they are used alongside Roman numerals.

After this point, the popularity of Arabic numerals increased and hence the usage of Roman numerals declined. Still, Roman numerals were still widely used through the rest of the medieval period, and were sometimes preferred to Arabic numbers for their reasonable security against fraud when stating sums of money. For example, any digit of the number 2381, for example, can be altered to cause a substantial difference (as much as 7000 by changing the 2 to a 9), but the Roman equivalent MMCCCLXXXI cannot be easily altered to produce a new number.