The subtractive notation that is used when writing with Roman numerals

The additive notation that is used when writing with Roman numerals

IVXDCDDLLLIM: A group of numerals written in subtractive notation, of lower value, CD ( = 400), cannot precede a numeral of larger value, D ( = 500).

IVXDCDDLLLIM: The numeral (the letter) D ( = 500) cannot precede a numeral of larger value, M ( = 1,000).

IVXDCDDLLLIM: The numeral (the letter) L ( = 50) cannot precede a numeral of larger value, M ( = 1,000).

MMDXLIII

written as a Hindu-Arabic number

(the numbers we use every day)

The subtractive notation that is used when writing with Roman numerals

The additive notation that is used when writing with Roman numerals

How to convert the number 2,543

written as a Hindu-Arabic number

(the numbers we use every day)

### I = 1 (one); V = 5 (five);

### X = 10 (ten); L = 50 (fifty);

### C = 100 (one hundred);

### D = 500 (five hundred);

### M = 1,000 (one thousand);

### For larger numbers:

### (*) V = 5,000 or |V| = 5,000 (five thousand); see below why we prefer this notation: (V) = 5,000.

### (*) X = 10,000 or |X| = 10,000 (ten thousand); see below why we prefer this notation: (X) = 10,000.

### (*) L = 50,000 or |L| = 50,000 (fifty thousand); see below why we prefer this notation: (L) = 50,000.

### (*) C = 100,000 or |C| = 100,000 (one hundred thousand); see below why we prefer this notation: (C) = 100,000.

### (*) D = 500,000 or |D| = 500,000 (five hundred thousand); see below why we prefer this notation: (D) = 500,000.

### (*) M = 1,000,000 or |M| = 1,000,000 (one million); see below why we prefer this notation: (M) = 1,000,000.

(*) These numbers were written with an overline (a bar above) or between two vertical lines. Instead, we prefer to write these larger numerals between brackets, ie: "(" and ")", because:

- 1) when compared to the overline - it is easier for the computer users to add brackets around a letter than to add the overline to it and
- 2) when compared to the vertical lines - it avoids any possible confusion between the vertical line "|" and the Roman numeral "I" (1).

(*) An overline (a bar over the symbol), two vertical lines or two brackets around the symbol indicate "1,000 times". See below...

Logic of the numerals written between brackets, ie: (L) = 50,000; the rule is that the initial numeral, in our case, L, was multiplied by 1,000: L = 50 => (L) = 50 × 1,000 = 50,000. Simple.

(*) At the beginning Romans did not use numbers larger than 3,999; as a result they had no symbols in their system for these larger numbers, they were added on later and for them various different notations were used, not necessarily the ones we've just seen above.

Thus, initially, the largest number that could be written using Roman numerals was:

**MMMCMXCIX = 3,999**.