# How to convert Arabic numbers to Roman numerals: breaking down into place value subgroups (units, tens, hundreds, thousands, etc.), in expanded notation

## Arabic numbers decomposing (breaking down) in place value subgroups before converting to Roman numerals:

• To 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..
• Convert each of these subgroups separately to numbers written down with Roman numerals;
• Wrap it up: catenate these subgroups using the additive notation to get the end Roman numeral.

## 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).