Is the entered Roman number, (X)M(V)XXI, valid or not?
How to convert the Roman number:
(X)M(V)XXI
written as a Hindu-Arabic number
(the numbers we use every day)
1. The Roman numerals used to make the conversion:
I = 1; V = 5; X = 10; M = 1,000; (V) = 5,000; (X) = 10,000;
» The basic reading rules of the Roman numerals
The numerals and the groups of numerals written in subtractive notation must be written from left to right, in descending order of their values, from high to low. Some symbols (letters) can be repeated up to 3 times in a row: I, X, C, M, (X), (C), (M).
A group of Roman numerals written in subtractive notation = a group of two numerals (two letters), one of a lower value preceding another larger one. The only allowed subtractive groups are these: IV, IX, XL, XC, CD, CM, M(V), M(X), (X)(L), (X)(C), (C)(D), (C)(M). To calculate the value of a group subtract the value of the first symbol from the value of the second.
» The subtractive notation that is used when writing with Roman numerals
A group of Roman numerals written in additive notation = a group of two or more numerals (letters), either of equal value or sorted in descending order of their values from high to low. To calculate the value of the group, add up the values of the symbols that make up the group.
» The additive notation that is used when writing with Roman numerals
(X)M(V)XXI is a valid Roman numeral.
(X)M(V)XXI 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:
(X)M(V)XXI
M(V) = (V) - M = 5,000 - 1,000 = 4,000;
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:
(X)M(V)XXI =
(X) + M(V) + X + X + I =
10,000 + 4,000 + 10 + 10 + 1 =
14,021
Check the result (reverse the process).
How to convert the number 14,021
1. Break the number into place value subgroups (decompose it):
14,021 =
10,000 + 4,000 + 20 + 1;
2. Convert each subgroup:
10,000 = (X);
4,000 = 5,000 - 1,000 = (V) - M = M(V);
20 = 10 + 10 = X + X = XX;
1 = I;
3. Wrap up the Roman numeral (construct it):
14,021 =
10,000 + 4,000 + 20 + 1 =
(X) + M(V) + XX + I =
(X)M(V)XXI
(X)M(V)XXI is a valid Roman numeral.
(X)M(V)XXI = 14,021
(X)M(V)XXI
written as a Hindu-Arabic number
(the numbers we use every day)
(X)M(V)XXI is a group of numerals written in both additive and subtractive notation.
How to convert other Roman numerals:
» How to convert the Roman number: (X)M(V)XX = ? Roman Numerals (Numbers) Validator
» How to convert the Roman number: (X)M(V)XXII = ? Roman Numerals (Numbers) Validator
Validate and convert Roman numerals to Hindu-Arabic numbers
Learn how to convert Roman numerals to Hindu-Arabic numbers:
Identify and calculate the value of each group of numerals written in subtractive notation.
Calculate the Hindu-Arabic number: add up all the values of the individual Roman numerals (written in additive notation) and of the groups of numerals written in subtractive notation.
The set of basic symbols of the Roman system of writing numerals
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:
- MMMCMXCIX = 3,999.
