# Roman numbering system

##### Article

November 30, 2021

The Roman numbering system is an additive / subtractive numbering system for which each literal symbol is associated with a value: the number represented is given by the sum or difference of the values ​​of each symbol that composes it.

## Basic symbols

Roman numerals are sequences of symbols, each of which identifies a number. The following table lists the Roman symbols alongside their corresponding values ​​expressed in the decimal number system. Note that there is no symbol to express zero Ⅰ 1 V 5 X 10 L 50 C 100 D 500 M 1 000

## Suffixes for multiples

The Roman system made use of frame suffixes to indicate notable multiples. By superlining or underlining a letter, its original value is multiplied by 1 000. This has similarities with the Prefixes of the International System of Units. I 1 000 V 5 000 X 10 000 L 50 000 C 100,000 D 500,000 M 1 000 000 Bordering a letter with two vertical lines at its sides and a horizontal line above it, its original value is multiplied by one hundred thousand. The ancient Romans did not have a specific word for either the millions or the billions and their maximum numerical lexical expression was the thousands. For example, 1 000 000 was referred to as "one thousand thousand". I 100 000 V 500,000 X 1 000 000 L 5,000,000 C 10 000 000 D 50,000,000 M 100 000 000 Bordering with two horizontal lines above, the original value is multiplied by 1 000 000. I 1 000 000 V 5,000,000 X 10 000 000 L 50,000,000 C 100,000,000 D 500,000,000 M 1 000 000 000

## Rules

To obtain the other expressible integers, these symbols must be combined, i.e. juxtaposed, in order to obtain strings that respect the following rules. Within a Roman numeral the symbols I, X, C and M can be repeated consecutively, as a rule, at most three times, while the symbols V, L and D can never be inserted more than once in a row. However, there are also forms with four symbols, such as the four IIII, which is reported in some ancient epigraphs of Lazio (such as in the 76 of the 80 entrances of the Colosseum intended for the public) and of Etruria (above all) and in other areas. However, it should be emphasized that some epigraphs found in Pompeii show the four in the medieval form IV. A sequence (ie a string) of symbols that never presents increasing values ​​denotes the integer obtained by adding the values ​​of the symbols indicated (principle of addition by juxtaposition); examples II 2, XI 11, XVIII 18, CXV 115, DLII 552, MMXVIII 2018. When a symbol is encountered followed by a second symbol of greater value, the result is the difference between the two (difference principle); examples: IV 4, IX 9, XL 40, XC 90, CD 400, CM 900. Strings made up of pairs of the previous type and symbols are also acceptable, as long as you switch from a pair to a pair of lower value, from a symbol to a pair of both lower symbols, and from a pair to a lower symbol of both members of the pair . Only I, X and C can be used in a subtractive sense. These rules mean that certain numbers can be expressed in more than one way: for these cases the more concise writing is preferable. The following sets of successive numbers are therefore identified (to) 1 I 2 II 3 III 4 IV 5 V 6 VI 7 VII 8 VIII 9 IX (a09): (a) as a silent string, that is a string that juxtaposed to another leaves it unchanged. (a08): (a09) private of IX. (b) includes X and the strings obtained by making X follow a string of the set (a), that is, the strings obtained by juxtaposing X and a string of (a09): 10 X 11 XI 12 XII 13 XIII 14 XIV 15 XV 16 XVI 17 XVII 18 XVIII 19 XIX (c) numbers between 20 and 29: juxtapositions of X and a string of (b) (d) numbers between 30 and 39: juxtapositions of X and

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