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the numerals of the ancient Romans. The Roman numeral system makes use of special symbols for powers of the base ten; for example, I = 1, × = 10, C = 100, and M = 1,000. Symbols also exist for halves of certain decimal powers: V = 5, L = 50, and D = 500. The natural numbers are written by means of the repetition of these numerals. If a larger numeral stands before a smaller one, the additive principle applies—that is, the numbers represented by the two numerals are added together. If a smaller numeral precedes a larger one, the subtractive principle applies—the smaller number is subtracted from the larger. The subtractive principle is made use of only to avoid repeating the same numeral four times. For example, I, X, and C are placed before X, C, and M, respectively, to signify 9, 90, and 900; when I, X, and C stand before V, L, and D, respectively, the numbers symbolized are 4, 40, and 400. Some examples of the expression of numbers in this system follow: VI = 5 + 1 = 6, IV = 5 – 1 = 4 (instead of IIII), XIX = 10 + 10 – 1 = 19 (instead of XVIIII), XL = 50 – 10 = 40 (instead of XXXX), and XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33.
The Roman numeral system is very inconvenient for arithmetic operations with multidigit numbers. It is used today only in a few special cases. For example, it is occasionally used to designate centuries (the XVth century is the 15th century), years of the Common Era (MCMLXXV is the year 1975), months in dates (the Russian expression 1.V.1975 means May 1, 1975), ordinal numbers, and derivatives whose order is low but greater than three (such as in yIV and y v).