Roman Numerals
Table 1 shows all the symbols used in the Roman numeral system
| Roman Numeral System | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Main Rules for the Roman Numeral System
Roman numerals should be arranged in descending order from largest to smallest, from left to right.
- Example 1: CLX (160): C (100) is followed by L (50) and X (10), arranged in descending order.
- Example 2: MCMXL (1940): M (1000) is followed by CM (900), and then XL (40), all arranged in descending order.
Only the numerals I, X, C, and M can be repeated up to three times in succession. The numerals V, L, and D cannot be repeated.
- Example 1: XXX (30): X (10) is repeated three times.
- Example 2: CCC (300): C (100) is repeated three times.
- Invalid Example: VV (10): V (5) is incorrectly repeated, which is not allowed.
No symbol should be repeated more than three times. Instead, apply the subtraction rule to avoid exceeding this limit.
- Example 1: IV (4): Instead of repeating I four times (IIII), I is subtracted from V (5).
- Example 2: XL (40): Instead of repeating X four times (XXXX), X is subtracted from L (50).
Rules on Subtraction in Roman Numeral System
Only the symbols I, X, and C can be used for subtraction.
- Example 1: IX (9): I (1) is subtracted from X (10).
- Example 2: XC (90): X (10) is subtracted from C (100).
- Invalid Example: IC (99): This is incorrect because C (100) should only have X (10) subtracted, not I (1).
Only one symbol may be subtracted from a larger symbol.
- Example 1: XL (40): X (10) is subtracted from L (50), with only one subtraction.
- Example 2: CD (400): C (100) is subtracted from D (500), with only one subtraction.
- Invalid Example: XXC (80): This is incorrect because two X’s (20) should not be subtracted from C (100).
The symbol to be subtracted must precede the larger symbol.
- Example 1: IV (4): I (1) precedes V (5) for subtraction.
- Example 2: XC (90): X (10) precedes C (100) for subtraction.
- Invalid Example: VX (5): This is incorrect because V (5) cannot be subtracted from X (10).
The subtrahend (the symbol being subtracted) should be either one-fifth or one-tenth of the value of the minuend (the larger symbol).
- Example 1: IX (9): I (1) is one-tenth of X (10) and can be subtracted.
- Example 2: XL (40): X (10) is one-fifth of L (50) and can be subtracted.
- Invalid Example: XM (990): This is incorrect because X (10) cannot be subtracted from M (1000) as it does not represent one-fifth or one-tenth of M’s value.
If a smaller symbol follows the larger one, it must be less than the subtrahend.
- Example 1: XIV (14): I (1) is subtracted from V (5), and the remaining X (10) is larger than I.
- Example 2: XCIX (99): I (1) is subtracted from X (10) after C (100) is reduced by X (10), following the rule that any smaller symbol after the larger one must be less than the subtrahend.
- Invalid Example: IXL (39): This is incorrect because L (50) should not follow IX (9) directly.
Roman Numeral Exercises
Convert the following Roman Numerals
1. CCLX
2. DCCCVIII
3. DXXXVII
4. MXXXVI
5. CDLXXXVIII
Convert the following to Roman Numerals
1. 2,355
2. 295
3. 856
4. 499
5. 229
Answers
A.
1. 260
2. 808
3. 537
4. 1036
5. 488
B.
1. MMCCCLV
2. CCXCV
3. DCCCLVI
4. CDXCIX
5. CCXXIX
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