The Greatest Three-Digit Number in Roman Numerals

To determine the greatest three-digit number in Roman numerals, we need to understand the Roman numeral system and its rules. Roman numerals are composed of seven basic symbols: I, V, X, L, C, D, and M. Each symbol represents a specific value:

- I represents 1
- V represents 5
- X represents 10
- L represents 50
- C represents 100
- D represents 500
- M represents 1000

Understanding Roman Numerals

Roman numerals are written by combining these symbols and using certain rules:

1. Symbols can be repeated up to three times in a row. For example, III represents 3, XXX represents 30, and CCC represents 300.
2. When a smaller value symbol is placed before a larger value symbol, the smaller value is subtracted from the larger value. For example, IV represents 4 (V - I), IX represents 9 (X - I), and XL represents 40 (L - X).
3. When a smaller value symbol is placed after a larger value symbol, the smaller value is added to the larger value. For example, VI represents 6 (V + I), XI represents 11 (X + I), and LX represents 60 (L + X).

Identifying the Greatest Three-Digit Number

A three-digit number can range from 100 to 999. To determine the greatest three-digit number in Roman numerals, we can break it down into its hundreds, tens, and units places.

The hundreds place can have a value ranging from 100 to 900, represented by the symbols C, CC, CCC, CD, D, DC, DCC, DCCC, and CM. In Roman numerals, CM represents 900 and is the largest possible value in the hundreds place.

The tens place can have a value ranging from 10 to 90, represented by the symbols X, XX, XXX, XL, L, LX, LXX, LXXX, and XC. In Roman numerals, XC represents 90 and is the largest possible value in the tens place.

The units place can have a value ranging from 1 to 9, represented by the symbols I, II, III, IV, V, VI, VII, VIII, and IX. In Roman numerals, IX represents 9 and is the largest possible value in the units place.

The Greatest Three-Digit Number

By combining the largest possible values in each place, the greatest three-digit number in Roman numerals is CMXCIX.

- CM represents 900 in the hundreds place.
- XC represents 90 in the tens place.
- IX represents 9 in the units place.

Therefore, CMXCIX is the Roman numeral representation of the greatest three-digit number, which is 999 in the decimal system.