(D)(C)(C)(X)(X)M(X)CMXCIV is a valid Roman numeral.
(D)(C)(C)(X)(X)M(X)CMXCIV meets all the rules of writing Roman numerals.
2. Identify the groups of symbols written in subtractive notation.
Identify and calculate the value of each group of any two symbols (any two letters) written in subtractive notation:
(D)(C)(C)(X)(X)M(X)CMXCIV
M(X) = (X) - M = 10,000 - 1,000 = 9,000;
CM = M - C = 1,000 - 100 = 900;
XC = C - X = 100 - 10 = 90;
IV = V - I = 5 - 1 = 4;
3. Calculate the value of the Roman number.
Add up all the values of the individual Roman numerals and of the groups of numerals written in subtractive notation:
(D)(C)(C)(X)(X)M(X)CMXCIV =
(D) + (C) + (C) + (X) + (X) + M(X) + CM + XC + IV =
500,000 + 100,000 + 100,000 + 10,000 + 10,000 + 9,000 + 900 + 90 + 4 =
729,994
(D)(C)(C)(X)(X)M(X)CMXCIV is a group of numerals written in additive and subtractive notation.
Check the result (reverse the process).
How to convert the number 729,994
1. Break the number down to place value subgroups (decompose it):
729,994 =
700,000 + 20,000 + 9,000 + 900 + 90 + 4;
2. Convert each subgroup:
700,000 = 500,000 + 100,000 + 100,000 = (D) + (C) + (C) = (D)(C)(C);
20,000 = 10,000 + 10,000 = (X) + (X) = (X)(X);
9,000 = 10,000 - 1,000 = (X) - M = M(X);
900 = 1,000 - 100 = M - C = CM;
90 = 100 - 10 = C - X = XC;
4 = 5 - 1 = V - I = IV;
3. Wrap up the Roman numeral (construct it):
729,994 =
700,000 + 20,000 + 9,000 + 900 + 90 + 4 =
(D)(C)(C) + (X)(X) + M(X) + CM + XC + IV =
(D)(C)(C)(X)(X)M(X)CMXCIV;
The final answer:
The major set of symbols on which the rest of the Roman numberals were built:
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: