Number System - Roman Numerals

The Roman numeral system uses seven basic capital letters of the English alphabet as symbols: $I = 1$, $V = 5$, $X = 10$, $L = 50$, $C = 100$, $D = 500$, and $M = 1000$. Unlike our standard Hindu-Arabic system, there is no symbol for zero in Roman numerals.

Rule of Repetition: When a symbol is repeated, its value is added as many times as it occurs. For example, $II = 1 + 1 = 2$ and $XXX = 10 + 10 + 10 = 30$. Note that the symbols $I$, $X$, $C$, and $M$ can be repeated a maximum of three times, whereas $V$, $L$, and $D$ are never repeated.

Rule of Addition: If a symbol of smaller value is written to the right of a symbol of greater value, we add their values. Imagine a ladder where the steps go down in value: $VI = 5 + 1 = 6$ and $LX = 50 + 10 = 60$.

Rule of Subtraction: If a symbol of smaller value is written to the left of a symbol of greater value, we subtract the smaller value from the greater value. For example, $IV = 5 - 1 = 4$ and $XC = 100 - 10 = 90$.

Constraints on Subtraction: The symbols $V$, $L$, and $D$ are never subtracted. The symbol $I$ can be subtracted from $V$ and $X$ only. The symbol $X$ can be subtracted from $L$ and $C$ only. For example, to write $95$, we cannot write $VC$; we must write $90 + 5 = XCV$.

Writing Large Numbers: To write numbers greater than $10$ in Roman numerals, we first break the number into thousands, hundreds, tens, and ones. For example, $48$ is viewed as $40 + 8$, which is written as $(50 - 10) + (5 + 3) = XLVIII$.