What is 240 in Roman Numerals?

The Roman numeral for 240 is CCXL. This representation is derived by combining the symbols for 200 and 40, adhering to the established rules of the Roman numeral system.

Understanding the Formation of CCXL

To express 240 in Roman numerals, the number is typically broken down into its constituent parts that correspond to Roman symbols. For 240, this involves recognizing:

• 200: Represented by CC (C + C), where 'C' stands for 100.
• 40: Represented by XL (L - X), where 'L' stands for 50 and 'X' stands for 10. This showcases the subtractive principle.

Therefore, combining these parts, 240 is written as CCXL because CC + XL equals 200 + 40.

Basic Roman Numeral Values

The Roman numeral system uses a combination of seven basic symbols to represent numbers. Here are their values:

Principles of Roman Numeral Construction

Numbers in the Roman system are formed using two primary principles:

• Additive Principle

  When a symbol of a smaller value follows a symbol of a larger value, their values are added together.

  • Example: VI = 5 (V) + 1 (I) = 6
  • Example: LX = 50 (L) + 10 (X) = 60
  • Example: CC = 100 (C) + 100 (C) = 200

• Subtractive Principle

  When a symbol of a smaller value precedes a symbol of a larger value, the smaller value is subtracted from the larger one. This rule is applied for certain combinations to avoid repeating more than three identical symbols (e.g., IIII for 4 is avoided in favor of IV).

  • Example: IV = 5 (V) - 1 (I) = 4
  • Example: XL = 50 (L) - 10 (X) = 40
  • Example: CM = 1000 (M) - 100 (C) = 900

Applying these principles, the number 240 is precisely represented as CCXL, combining the additive nature for 200 and the subtractive rule for 40.