Roman Numerals

Landmark Numbers

The Roman system uses specific letters as landmark numbers.

Rules of Formation

1. Addition: Symbols placed after a larger one are added ($VI = 5 + 1 = 6$).
2. Subtraction: Symbols placed before a larger one are subtracted ($IV = 5 - 1 = 4$).
3. Repetition: Symbols (I, X, C, M) can be repeated up to 3 times ($XXX = 30$). V, L, D are never repeated.

Arithmetic Difficulty

Adding Roman numerals is cumbersome because it involves grouping and regrouping letters rather than simple column addition.

Example: $27 + 43$

• $27 = XXVII$
• $43 = XLIII$
• Summing Is: $II + III = V$
• Summing Xs: $XX + XL$ (This is hard to visualize directly without converting).

This difficulty paved the way for better systems.