The Roman numeral XC represents the number 90.
Understanding Roman Numerals and the Subtraction Rule
Roman numerals are a numerical system that originated in ancient Rome. Unlike our modern decimal system, Roman numerals use combinations of letters from the Latin alphabet to denote values. A key aspect of this system is the principle of subtraction, which applies when a smaller value numeral precedes a larger value numeral.
How to Calculate XC
The Roman numeral XC is an excellent example of the subtraction rule in action. To determine its value, we break down its components:
- X represents the number 10.
- C represents the number 100.
When a smaller numeral (X) appears immediately before a larger numeral (C), the value of the smaller numeral is subtracted from the value of the larger numeral.
Therefore, the calculation is as follows:
- Value of C = 100
- Value of X = 10
- XC = C - X = 100 - 10 = 90
This method prevents the need for four identical numerals in a row (e.g., LXXXX for 90, which is incorrect). Instead, the more concise and efficient XC is used.
Common Roman Numeral Values
Understanding the basic values of Roman numerals helps in deciphering more complex combinations:
| Roman Numeral | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Key Principles of Roman Numerals
When working with Roman numerals, remember these fundamental rules:
- Addition: If a numeral of equal or greater value precedes a numeral of smaller value, their values are added (e.g., VI = 5 + 1 = 6, LX = 50 + 10 = 60).
- Subtraction: As seen with XC, if a numeral of smaller value precedes one of larger value, the smaller is subtracted from the larger. This rule typically applies to specific pairs:
- I can precede V (IV = 4) and X (IX = 9).
- X can precede L (XL = 40) and C (XC = 90).
- C can precede D (CD = 400) and M (CM = 900).
- Repetition: A numeral can be repeated up to three times to indicate multiplication of its value (e.g., III = 3, XX = 20, CCC = 300). V, L, and D are never repeated.
- No more than three repetitions: Except for some historical variations, generally no more than three identical numerals are used consecutively.
By applying these rules, any number can be accurately converted to or from Roman numerals.
