DCCCXLIIICXIXCIII: Roman Numeral Converted to Number

Is the Roman number DCCCXLIIICXIXCIII valid (written correctly)?
How to convert it into its decimal equivalent number?

To validate and convert the Roman number DCCCXLIIICXIXCIII into its decimal equivalent - the so called Arabic number, that we use all the time, we must identify its individual symbols and groups of symbols. Detailed explanations below

1. The Roman numerals used to make the conversion:

I = 1; X = 10; L = 50; C = 100; D = 500;

» 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. Example: IV = V - I = 5 - 1 = 4.
» 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 and from left to right. To calculate the value of the group, add up the values of the symbols that make up the group. Example: II = I + I = 2.
» The additive notation that is used when writing with Roman numerals


2. The groups of numerals written in subtractive notation:

DCCCXLIIICXIXCIII

XL = L - X = 50 - 10 = 40;

IX = X - I = 10 - 1 = 9;


DCCCXLIIICXIXCIII is not a valid Roman numeral.

3. Why is the Roman numeral not valid?

DCCCXLIIICXIXCIII: A group of numerals written in subtractive notation, of lower value, XL ( = 40), cannot precede a numeral of larger value, C ( = 100).

DCCCXLIIICXIXCIII: The numeral (the letter) I ( = 1) cannot precede this numeral of larger value, C ( = 100). I may only precede the numerals V ( = 5) and X ( = 10).

DCCCXLIIICXIXCIII: A group of numerals written in subtractive notation, of lower value, IX ( = 9), cannot precede a numeral of larger value, C ( = 100).


4. Please correct or remove (some of) the symbols numerals:

DCCCXLIIICXIXCIII


Instead,
How to convert the Roman number:
MLXIII
written as an Arabic number
(the numbers we use every day)

1. The Roman numerals used to make the conversion:

I = 1; X = 10; L = 50; M = 1,000;

» The basic reading rules of the Roman numerals

MLXIII is a valid Roman numeral.

MLXIII meets all the rules for writing Roman numerals.


2. Calculate the value of the Roman number.

Add up all the values of the individual Roman numerals (the values of the letters):


MLXIII =

M + L + X + I + I + I =

1,000 + 50 + 10 + 1 + 1 + 1 =

1,063

DCCCXLIIICXIXCIII is not a valid Roman numeral.

Instead, this numeral is valid:
MLXIII = 1,063

MLXIII
written as an Arabic number
(the numbers we use every day)

MLXIII is a group of numerals written in additive notation.

How to convert other Roman numerals:

» How to convert the Roman number: MXXXVII = ? Roman Numerals (Numbers) Validator

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Validate and convert Roman numerals to Hindu-Arabic numbers

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.