Roman numerals reading rules: online lesson for learning how to write Arabic numbers by using Roman numerals

Introduction

Although within the Roman Empire itself it was enforced a set of stricter rules that would have lead to the standardization of Roman numerals writing, in the last hundred years some rules were applied to eliminate confusion.

We concluded that there is a set of six rules to be remembered about Roman numerals.
Read them below, in order. Don't worry if you don't understand something right away. When you finish reading all the six rules, things will become clearer.

1) The first rule - the set of basic symbols in Roman writing

The major numerals, symbols on which to build the rest of the numbers in Roman system are:
  • 1 = I (one)
  • 5 = V (five)
  • 10 = X (ten)
  • 50 = L (fifty)
  • 100 = C (one hundred)
  • 500 = D (five hundred)
  • 1000 = M (one thousand)
  • 5000 = (V) (five thousand) *
  • 10,000 = (X) (ten thousand) *
  • 50,000 = (L) (fifty thousand) *
  • 100,000 = (C) (one hundred thousand ) *
  • 500,000 = (D) (five hundred thousand) *
  • 1,000,000 = (M) (one million) *

* The number was also written with a bar above or between two vertical bars, to indicate multiplying that number by 1,000. We prefer writing in brackets because it is more accessible to computer users and for avoiding any possible confusion with the symbol for one - I.

At first, the Romans did not use numbers higher than 3999, having no representation for numbers 5,000, 10,000, 50,000, 100,000, 500,000, 1,000,000. These were added later on and for them various different notations were used, not necessarily the ones above. Thus, initially, the maximum number that could be written with Roman numerals was: MMMCMXCIX (3999).

2) The second rule - numerals repetition

Rule of Roman numerals repetition in a number
  • these symbols: I (1), X (10), C (100), M (1,000), (X) (10,000), (C) (100,000), (M) (1,000,000) may occur no more than three times in succession in a number.
  • these symbols: V (5), L (50), D (500), (V) (5,000), (L) (50,000), (D) (500,000) may appear only once in a number.
For instance:
  • Number 4 is written as a numeral: IV and not IIII (though the IIII form circulated as an additive form)
  • Number 5 is written as a numeral: V and not IIIII
  • Number 10 will be written: X and not VV
  • Number 100 will be written: C and not XXXXXXXXXX, or LXXXXX, or LL etc.

3) The third rule - the subtraction

Subtraction rule - a numeral of lesser value placed before a larger value numeral is subtracted from the latter. Only these symbols are allowed to subtract from a larger value: I (1), X (10), C (100), M (1,000), (X) (10,000), (C) (100,000), (M) (1,000,000). These numerals are NOT used to subtract from larger values: V (5), L (50), D (500), (V) (5,000), (L) (50,000), (D) (500,000).
Example:
  • Number four (4) is written by using two important symbols listed under the first rule above: I (1) and V (5), subtracting I from V, by placing I ahead of the V symbol. We thus obtain: IV (4).
  • Number nine (9) is written by using two important symbols listed under the first rule, above: I (1) and X (10), subtracting I from X by placing I ahead of X symbol. We thus obtain: IX (9).

4) The fourth rule - addition

Addition rule - a numeral of lesser value placed after another one of greater value or equal, add to the latter. The fourth rule outweigh the third rule, of subtraction, when writing Roman numerals. Only if a number can not be built by adding, subtraction rule applies.
Example:
  • Number two (2) is written by using a single important symbol listed under the first rule: I (1). Placing the I symbol after another I symbol leads to: II (2)
  • Number three (3) is written by placing I symbol after II (2), so we obtain: III (3)
  • Number six (6) is written by placing the I symbol (1) after the V symbol (5), we obtain: VI (6)
  • Number seven (7) is written by placing the symbol I (1) after the symbol V (5) twice, so we obtain: VII (7)
  • Number eight (8) is written by placing the symbol I (1), after the symbol V (5), three times, to get: VIII (8) - and NOT IIX
  • Number eleven (11) is written by adding I (1) to X (10), by placing the symbol I (1) after the symbol X (10), to obtain: XI (11)
  • Number Twenty (20) is written by adding X (10) after another X (10), to obtain: XX (20)

5) The fifth rule - the order of magnitude of the numeral used to subtract from a larger value numeral

Although this rule is an addition to the third rule, of the subtraction, we preferred to treat it separately because it is very important to be understood correctly.

Order of magnitude of the numeral used to subtract from a larger value numeral - Romans, as a rule, put in front of a number of tens value, only one of units value, for a number of hundreds value only one of tens value, for one of the thousands only one of the hundreds, and so on ... They put in front of a number another one that was immediately below in the basic set of symbols: I (1), X (10), C (100), M (1,000), (X) (10,000), (C) (100,000), (M) (1,000,000). Numbers V (5), L (50), D (500), (V) (5,000), (L) (50,000), (D) (500,000) were not used to decrease numbers' value by positioning them in front of other higher numbers.
Example:
  • 99 is written XCIX and not IC (thus subtracting I from X to get 9, X from C to get 90, then add IX to XC by placing it after XC and obtaining XCIX - and not subtracting I directly from C. Correct form: 99 = XCIX / Wrong forbidden form: 99 = IC
  • 95 is written as XCV, and not VC.

6) The sixth rule - the decomposition of numbers

Rule of decomposition and transformation of Arabic numbers into Roman numerals - to turn any Arabic number into a Roman numeral, the rule is to break down that number into subgroups, by units, tens, hundreds, thousands, ten of thousands, hundred of thousands, millions, etc.. and so to transform each of these subgroups separately, then assemble them according to the rule of addition.
Example:
  • 19 = 10 + 9 = 10 + (10 - 1) = X + IX = XIX (not IXX)
  • 39 = 30 + 9 = (10 + 10 + 10 ) + (10-1) = XXX + IX = XXXIX (not IXL)
  • 42 = 40 + 2 = (50 - 10) + 2 = XL + II = XLII
  • 79 = 70 + 9 = (50 + 20) + (10 - 1) = LXX + IX = LXXIX (not ILXXX)
  • 99 = 90 + 9 = (100 - 10) + (10 - 1 ) = XC + IX = XCIX (not IC)
  • 104 = 100 + 0 + 4 = C + IV = CIV
  • 120 = 100 + 20 + 0 = C + XX = CXX
  • 150 = 100 + 50 = CL
  • 173 = 100 + 70 + 3 = 100 + (50 + 20) + 3 = C + LXX + III = CLXXIII
  • 199 = 100 + 90 + 9 = 100 + (100 - 10) + (10 - 1) = C + XC + IX = CXCIX (not ICC, not CIC)
  • 200 = CC
  • 207 = 200 + 0 + 7 = 200 + (5 + 2) = CC + VII = CCVII
  • 267 = 200 + 60 + 7 = 200 + (50 + 10) + (5 + 2) = CCLXVII
  • 448 = 400 + 40 + 8 = (500 - 100) + (50 - 10) + 8 = CD + XL + VIII = CDXLVIII
  • 503 = 500 + 3 = D + III = DIII
  • 944 = 900 + 40 + 4 = (1,000 - 100) + (50 - 10) + (5 - 1) = CM + XL + IV = CMXLIV
  • 1,973 = 1,000 + 900 + 70 + 3 = 1,000 + (1,000 - 100) + (50 + 20) + 3 = M + CM + LXX + III = MCMLXXIII
  • 2,012 = 2,000 + 10 + 2 = MM + X + II = MMXII
  • 3,999 = 3,000 + 900 + 90 + 9 = 3,000 + (1,000 - 100) + (100 - 10) + (10 - 1) = MMM + CM + XC + IX = MMMCMXCIX
  • 4,000 = 5,000 - 1,000 = (V) - M = M(V)

More examples of converting Arabic numbers into Roman numerals:

  • 2 = II, 3 = III, 4 = IV, 6 = VI, 7 = VII, 8 = VIII, IX = 9, 11 = 10 + 1 = XI, 12 = 10 + 2 = XII, 13 = 10 + 3 = XIII, 14 = 10 + 4 = XIV
  • 47 = 40 + 7 = XL + VII = XLVII
  • 79 = 70 + 9 = LXX + IX = LXXIX
  • 469 = 400 + 60 + 9 = CD + LX + IX = CDLXIX
  • 2,000 = MM
  • 2,010 = 2,000 + 10 = MMX
  • 2,234 = 2,000 + 200 + 30 + 4 = MM + CC + XXX + IV = MMCCXXXIV
  • 4,787 = 4,000 + 700 + 80 + 7 = M (V) + DCC + LXXX + VII = M(V)DCCLXXXVII
  • 6,787 = 6,000 + 700 + 80 + 7 = (V)M + DCC + LXXX + VII = (V)MDCCLXXXVII
  • 30,924 = 30,000 + 900 + 20 + 4 = (X)(X)(X) + CM + XX + IV = (X)(X)(X)CMXXIV
  • 3,999,893 = 3,000,000 + 900,000 + 90,000 + 9,000 + 800 + 90 + 3 = (M)(M)(M) + (C)(M) + (X)(C) + M(X) + DCCC + XC + III = (M)(M)(M)(C)(M)(X)(C)M(X)DCCCXCIII
  • Date 1: 2012-Oct-17 = 2012-10-17 = XXII-X-XVII
  • Date 2: 1863-Aug-29 = 1863-8-29 = (1,000 + 800 + 60 + 3)-8-29=(M + DCCC + LX + III)-VIII-XXIX = MDCCCLXIII-VIII-XXIX