Knowing Our Numbers - Roman Numerals

Basic Symbols: The Roman numeral system uses seven primary symbols to represent numbers: $I = 1$, $V = 5$, $X = 10$, $L = 50$, $C = 100$, $D = 500$, and $M = 1000$. These act as the building blocks for all other numbers.

Rule of Repetition: When a symbol is repeated, its value is added as many times as it occurs (e.g., $II = 2$ and $XXX = 30$). However, a symbol cannot be repeated more than three times in a row. Imagine a stack of up to three identical blocks; to represent four, a different subtraction-based structure is needed.

Non-repeatable Symbols: The symbols $V$, $L$, and $D$ are unique because they are never repeated. You will never see $VV$ for $10$ because $X$ is used instead.

Rule of Addition: If a symbol of smaller value is placed to the right of a symbol of greater value, we add their values. For example, in $XVI$, we see $10 + 5 + 1 = 16$. Visually, this looks like a large value followed by descending smaller values.

Rule of Subtraction: If a symbol of smaller value is placed to the left of a symbol of greater value, its value is subtracted from the larger symbol. For example, $IV = 5 - 1 = 4$ and $IX = 10 - 1 = 9$. This is used to avoid repeating a symbol four times.

Subtraction Constraints: Subtraction follows specific pairings: $I$ can only be subtracted from $V$ and $X$; $X$ can only be subtracted from $L$ and $C$; and $C$ can only be subtracted from $D$ and $M$. Symbols $V, L,$ and $D$ are never subtracted from any larger symbol.

Number Composition: To write large Hindu-Arabic numbers in Roman numerals, decompose the number into thousands, hundreds, tens, and ones. For example, $48$ is viewed as $40 + 8$, which is $(50 - 10) + (5 + 3)$, resulting in $XLVIII$.