# What are the rules of Roman numerals

## Roman numerals

Today, Roman numbers or Roman numerals are mainly found in the form of years on historical buildings or in documents, as years were often given in this way centuries after the fall of the Roman Empire. Furthermore, Roman numbers are also used in chronograms to distinguish rulers of a dynasty with the same first name, to number the levels of structure in books and documents, or to entertain the so-called "matchstick puzzles".

Program: Converter to and from Roman numerals

### Roman numerals converter

Use this program to convert from decimal to Roman numerals and vice versa. Any errors or warnings are displayed in the Comments field. Wear the Roman number in the blue or green field and click on the corresponding arrow. The number converted into decimal is then displayed in the upper field. To convert a decimal number into a Roman one, enter it in the upper field and press the brown arrow.

 Basic character (GZ) Auxiliary sign (HZ) character Valence character Valence I. 1 V. 5 X 10 L. 50 C. 100 D. 500 M. 1000
Figure 1: Basic and auxiliary symbols

### Roman numerals

The roman number system is in contrast to ours today Place value system a so-called Addition system. In a place value system, the value of a digit also depends on its position within the number (e.g. 3531 = digit 3 has one value 3000 and one value 30). On the other hand, every digit or every character in an addition system has the same value, regardless of its occurrence within the numeric word. Addition system also means that the value of the numeric word is determined by adding the values ​​of all characters listed.

Figure 3: Signs of higher significance

Figure 1 shows the basic and auxiliary symbols that are used for representation. The valence of the basic and auxiliary characters is added. However, the auxiliary characters are an exception. Their value is subtracted in the corresponding position in the number word (see "Subtractive combination" below). This was only introduced later for the sake of simplicity and was not originally part of this number system.

Figure 2: Multipliers

The Number 0 could not be displayed. However, this is also not necessary in an addition system. In this case, the word "zero", "none", "nothing", etc. was simply used to indicate quantities.

The most common way of displaying larger numbers is to use multipliers. Numbers underlined correspond to the value of the numeric word multiplied by 1,000, framed numeric words to a multiplication by 100,000. Figure 2 shows these variants.

There are also additional characters with higher weights. Usually these are compound characters that can also be displayed in combination. A mirrored "C" is mostly used. In conjunction with an "I", it is also represented as a "D". Figure 3 shows number signs up to 100,000.

### Examples of Roman numerals

Table 1 shows examples of Roman numerals.

 Decimal Roman Roman Decimal Roman Roman Decimal Roman Roman 1 I. I. 11 XI XI 70 LXX LXX 2 II II 12 XII XII 80 LXXX LXXX 3 III III 13 XIII XIII 90 XC XC 4 IV IV ... ... ... 98 XCVIII XCVIII 5 V. V. 19 XIX XIX 99 IC XCIX 6 VI VI 20 XX XX 100 C. C. 7 VII VII 30 XXX XXX 110 CX CX 8 VIII VIII 40 XL XL 200 CC CC 9 IX IX 50 L. L. 999 IN THE CMXCIX 10 X X 60 LX LX 1000 M. M.
Table 1: Examples of Roman numerals

### Detailed display rules

The following rules apply to reading and writing Roman numerals. Here, however, you have to consider 2 different variants. On the one hand the general rules and on the other hand, those mainly taught in schools Additions to the rules.

 1 The basic unit of a Roman numeral is supposed to be the "Roman numeral" RZ are designated. According to this, a Roman numeral consists of a sequence of RZ. Example: Roman numerals = MMDIX consists of the RZ: "M", "M", "D", "IX"

 2 A RZ is either a basic sign GZ, an auxiliary character HZ or a "subtractive combination" SK (Definition SK see rules 7-9). Example: MMDIX consists of the following RZ: "M" = GZ, "M" = GZ, "D" = HZ, "IX" = SK

 3 Each RZ has a defined value. For GZ and HZ the valence is given in the table above. For SK the value can be found in rules 7-9. Example: value of HZ "V" is 5 Example: value of SK "IV" is 4

 4 In a Roman numeral are the individual RZ sorted from left to right in descending order. Ex: MDCCXIII (M> D> C> X> I)

 5 The value of a Roman numeral is determined by the sum of the valencies of the individual RZ Example: MDVII = 1000 + 500 + 5 + 1 + 1 = 1507

 6 A RZ from the same GZ may not exceed 3 times and from the same HZ as well as from the same SK may appear at most once. The number 4 (= IIII) on clock faces is an exception. Example: 66 is not XXXXXXIIIIII but LXVI

 7 A SK consists of 2 characters, one being GZ to the left of one GZ or HZ greater value. Example: XD = GZ X is facing HZ D; important: D has a higher value than X Special rule: (mainly taught in schools) I only precedes V and X X only precedes L and C C only precedes D and M

 8 The resulting value of a SK is the difference between the weights of the two contained GZ and or HZ. Ex: XD = 490; IC = 99; IV = 4

 9 To the right of one SK may only RZ follow which GZ and or HZ contain that have a lower valence than the left component of said SK. Ex: wrong: XCIX = 99; correct: IC = 99 When observing the special rule 7, this applies Rule 9 Not. Ex: correct: XCIX = 99; wrong according to rule 7: IC = 99

 10 The additional characters ZZ can also with GZ and or HZ be combined. E.g: CI I. XCVIII = 1598

### Further pages

Conversion of (integer) decimal numbers into Roman numbers

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