A medieval system developed from a cruder Roman system. The system of Roman numerals is based on using special symbols to denote decimal digits $ I = 1 $,
$ X = 10 $,
$ C = 100 $,
$ M = 1000 $,
and their halves $ V = 5 $,
$ L = 50 $,
$ D = 500 $.
Positive integers are written by repeating these numerals. When a letter is followed by a letter of lesser value, the values are added (addition principle), when a letter is followed by a letter of greater value, the smaller is subtracted from the larger (subtraction principle). The latter rule is only applied in order to prevent a fourfold repetition of the same letter. In this system it is rather inconvenient to carry out arithmetic operations with multidigit numerals. At present, the Roman numerals are no longer used, except in certain cases such as the designation of centuries and years A.D. and also months when designating dates, ordinal numbers and sometimes derivatives of low order higher than three: $ y ^ {IV } , y ^ {V} $,
etc.
The cruder Roman system referred to above is as follows: $ 1000 $
was represented by $ 1 $
between parenthesis: $ ( 1) $;
$ 10 000 $
was represented by $ (( 1)) $,
etc. Later $ ( 1) $
became $ M $.
Half of it, $ {} 1) $,
later became $ D $.
A partial list of Roman numerals is:
<tbody> </tbody> $ 1 $
 I   $ 30 $
 XXX  $ 2 $
 II   $ 40 $
 XL or XXXX  $ 3 $
 III   $ 50 $
 L  $ 4 $
 IV or IIII   $ 60 $
 LX  $ 5 $
 V   $ 70 $
 LXX  $ 6 $
 VI   $ 80 $
 LXXX  $ 7 $
 VII   $ 90 $
 XC  $ 8 $
 VIII   $ 99 $
 XCIX or IC  $ 9 $
 IX or VIIII   $ 100 $
 C  $ 10 $
 X   $ 101 $
 CI  $ 11 $
 XI   $ 200 $
 CC  $ 12 $
 XII   $ 300 $
 CCC  $ 13 $
 XIII   $ 400 $
 CCCC  $ 14 $
 XIV   $ 500 $
 IO or D  $ 15 $
 XV   $ 600 $
 DC  $ 16 $
 XVI   $ 700 $
 DCC  $ 17 $
 XVII   $ 800 $
 DCCC  $ 18 $
 XVIII   $ 900 $
 DCCCC  $ 19 $
 XIX   $ 1000 $
 CIO or M  $ 20 $
 XX   $ 2000 $
 CIOCIO or MM 

<tbody> </tbody> $ 5000 $
 IOO  $ 10000 $
 CCIOO  $ 100000 $
 CCCIOOO  $ 500000 $
 IOOOO  $ 1000000 $
 CCCCIOOOO 

References
[a1]  G. Friedlein, "Die Zahlzeichen und das elementare Rechnen der Griechen und Römer und des Christlichen Abendlandes von 7. bis 13. Jahrhundert" , Schaan, reprint (1982) 
[a2]  G. Ifrah, "From one to zero: a universal history of numbers" , Penguin (1987) (Translated from French) 
[a3]  F. Cajori, "A history of mathematical notations" , 1 , Open Court (1974) 
How to Cite This Entry:
Roman numerals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Roman_numerals&oldid=48583
This article was adapted from an original article by BSE3 (originator), which appeared in Encyclopedia of Mathematics  ISBN 1402006098.
See original article