# The fourth rule: the additive notation that is used when writing Roman numerals

## The additive notation of the Roman numerals:

• A numeral placed immediately after another one of a larger or equal value (next to the right of it), is added to the latter. This is called additive notation.
• The fourth rule takes precedence over the third rule, that of the subtractive notation, when writing Roman numerals.
• Only if a number can no longer be constructed using the additive notation, taking into account rule no. 2, that of the repetition (the symbols may not be repeated more than three times in a row), only then the subtractive notation is applied.

## Example:

• Number 2 is written by placing the I (1) symbol after another I (1): 2 = 1 + 1 = I + I = II;
• Number 3 is also written by placing I (1) after I (1) twice: 3 = 1 + 1 + 1 = I + I + I = III;
• Instead, number 4 is NOT to be written by placing I (1) after I (1) 3 times: 4 = 1 + 1 + 1 + 1 = I + I + I + I = IIII because it would contradict rule no. 2 of the repetition of the numerals (a symbol can be repeated up to 3 times in a row), so 4 is constructed using the subtractive notation rule: 4 = 5 - 1 = V - I = IV;
• Number 6 is written by placing I (1) after V (5): 6 = 5 + 1 = V + I = VI;
• Number 7 is written by placing I (1) after V (5) twice: 7 = 5 + 1 + 1 = V + I + I = VII;
• Number 8 is written by placing I (1) after V (5) three times: 8 = 5 + 1 + 1 + 1 = V + I + I + I = VIII - not IIX;
• Instead, number 9 is NOT to be written by placing I (1) after V (5) four times: 9 = 5 + 1 + 1 + 1 + 1 = V + I + I + I + I = VIIII because it would contradict rule no. 2 of the repetition of the numerals (a symbol can be repeated up to 3 times in a row), so 9 is constructed using the subtractive notation: 9 = 10 - 1 = X - I = IX;
• Number 11 is written by adding I (1) to X (10), by placing I (1) after X (10): 11 = 10 + 1 = X + I = XI;
• Number 20 is written by placing X (10) after another X (10): 20 = 10 + 10 = X + X = XX;
• Number 104 is written by placing IV (4) after C (100) to get 104 = 100 + 4 = C + IV = CIV.