The sixth rule - Arabic numbers decomposing (breaking) into place value subgroups (units, tens, hundreds, thousands, etc.), in expanded notation, before converting to Roman numerals

Arabic numbers decomposing (breaking them down) before converting to Roman numerals:

  • To easily turn any Arabic number into a Roman numeral, break down that Arabic number (decompose it) into place value subgroups, in expanded notation, of units, tens, hundreds, thousands, ten of thousands, hundred of thousands, millions, etc..
  • Transform then each of these subgroups separately into numbers written with Roman numerals;
  • Wrap it up: reassemble these subgroups into the end Roman numeral according to the rule of addition.

Example:

  • 19 = 10 + 9 = 10 + (10 - 1) = X + IX = XIX;
  • 39 = 30 + 9 = (10 + 10 + 10) + (10 - 1) = (X + X + X) + (X - I) = XXX + IX = XXXIX;
  • 42 = 40 + 2 = (50 - 10) + (1 + 1) = (L - X) + (I + I) = XL + II = XLII;
  • 79 = 70 + 9 = (50 + 10 + 10) + (10 - 1) = (L + X + X) + (X - I) = LXX + IX = LXXIX;
  • 99 = 90 + 9 = (100 - 10) + (10 - 1) = (C - X) + (X - I) = XC + IX = XCIX;
  • 104 = 100 + 0 + 4 = 100 + (5 - 1) = C + (V - I) = C + IV = CIV;
  • 120 = 100 + 20 + 0 = 100 + (10 + 10) = C + (X + X) = C + XX = CXX;
  • 150 = 100 + 50 + 0 = C + L = CL;
  • 173 = 100 + 70 + 3 = 100 + (50 + 10 + 10) + (1 + 1 + 1) = C + (L + X + X) + (I + I + I) = C + LXX + III = CLXXIII;
  • 184 = 100 + 80 + 4 = 100 + (50 + 10 + 10 + 10) + (5 - 1) = C + (L + X + X + X) + (V - I) = C + LXXX + IV = CLXXXIV;
  • 200 = 200 + 0 + 0 = (100 + 100) = (C + C) = CC;
  • 207 = 200 + 0 + 7 = (100 + 100) + (5 + 1 + 1) = (C + C) + (V + I + I) = CC + VII = CCVII;
  • 267 = 200 + 60 + 7 = (100 + 100) + (50 + 10) + (5 + 1 + 1) = (C + C) + (L + X) + (V + I + I) = CCLXVII
  • 448 = 400 + 40 + 8 = (500 - 100) + (50 - 10) + (5 + 1 + 1 + 1) = (D - C) + (L - X) + (V + I + I + I) = CD + XL + VIII = CDXLVIII;
  • 503 = 500 + 0 + 3 = 500 + (1 + 1 + 1) = D + (I + I + I) = D + III = DIII;
  • 944 = 900 + 40 + 4 = (1,000 - 100) + (50 - 10) + (5 - 1) = (M - C) + (L - X) + (V - I) = CM + XL + IV = CMXLIV;
  • 1,973 = 1,000 + 900 + 70 + 3 = 1,000 + (1,000 - 100) + (50 + 10 + 10) + (1 + 1 + 1) = M + (M - C) + (L + X + X) + (I + I + I) = M + CM + LXX + III = MCMLXXIII;
  • 2,019 = 2,000 + 10 + 9 = (1,000 + 1,000) + 10 + (10 - 1) = (M + M) + X + (X - I) = MM + X + IX = MMXIX;
  • 3,999 = 3,000 + 900 + 90 + 9 = (1,000 + 1,000 + 1,000) + (1,000 - 100) + (100 - 10) + (10 - 1) = (M + M + M) + (M - C) + (C - X) + (X - I) = MMM + CM + XC + IX = MMMCMXCIX;
  • 4,000 = 5,000 - 1,000 = (V) - M = M(V).

Roman numerals reading rules, summary:


I. The first rule - Roman numerals set of basic symbols

II. The second rule - numerals repetition

III. The third rule - numerals subtraction

IV. The fourth rule - what numerals are allowed to be subtracted from larger value numerals

V. The fifth rule - numerals addition

VI. The sixth rule - Arabic numbers decomposing (breaking down) into place value subgroups, in expanded notation, before converting to Roman numerals


Examples of converting Arabic numbers into Roman numerals


Roman numerals from 1 to 100

Roman numerals from 1 to 1000