An ancient number system
The ancient Romans wrote numbers with letters. Roman numerals are still used today on clocks, book chapters, movie sequels, monarchs’ names (King Charles III) and the Super Bowl.
The seven symbols
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
There is no symbol for zero, and no place value like in our system.
Rule 1: Add when going from big to small
When symbols are written from largest to smallest, add them. This is the additive principle.
- VI = 5 + 1 = 6
- XV = 10 + 5 = 15
- LXX = 50 + 10 + 10 = 70
- MDC = 1,000 + 500 + 100 = 1,600
Rule 2: Subtract when small comes before big
When a smaller symbol comes just before a larger one, subtract it. This is the subtractive principle.
| Numeral | Meaning | Value |
|---|---|---|
| IV | 5 − 1 | 4 |
| IX | 10 − 1 | 9 |
| XL | 50 − 10 | 40 |
| XC | 100 − 10 | 90 |
| CD | 500 − 100 | 400 |
| CM | 1,000 − 100 | 900 |
Only these six pairs are used. I goes before V and X; X before L and C; C before D and M.
Rule 3: Repeat up to three times
I, X, C and M can repeat up to three times: III = 3, XXX = 30, CCC = 300. For 4, use IV, not IIII. V, L and D are never repeated.
(Some clock faces use IIII for 4. That’s a tradition, not the standard rule.)
Writing a number in Roman numerals
Break the number into thousands, hundreds, tens and ones, then convert each part.
Example: 1,994
- 1,000 = M
- 900 = CM
- 90 = XC
- 4 = IV
So 1,994 = MCMXCIV.
Reading Roman numerals
Go left to right. If a symbol is smaller than the next one, subtract it; otherwise add it.
Example: CXLVII = C (100) + XL (40) + V (5) + II (2) = 147.
Worked examples
Example 1: Write 14 in Roman numerals.
10 = X, 4 = IV → XIV.
Example 2: What is XXIX?
XX = 20, IX = 9 → 29.
Example 3: Write 2026.
MM = 2,000, XX = 20, VI = 6 → MMXXVI.
Common mistakes
- Writing four as IIII instead of IV.
- Subtracting from too far away: 99 is XCIX, not IC.
- Repeating V, L or D: 10 is X, not VV.
Try it yourself
- Write 8.
- Write 49.
- What is LXXIV?
- What is MCMLXX?
Answers: 1) VIII 2) XLIX 3) 74 4) 1970
Quick recap
- Seven symbols: I, V, X, L, C, D, M.
- Add big-to-small (additive principle); subtract small-before-big (subtractive principle).
- Repeat I, X, C, M at most three times.