The Roman numerals that we're going to use to make the conversion:
I = 1; V = 5; X = 10; L = 50; C = 100; D = 500; M = 1,000; (V) = 5,000; (L) = 50,000; (C) = 100,000; (D) = 500,000;
1. Break down the number.
Decompose the number, break it down to place value subgroups:
458,112 = 400,000 + 50,000 + 8,000 + 100 + 10 + 2;
2. Convert each subgroup.
Convert each of the place value subgroups, write them in Roman numerals:
400,000 = 500,000 - 100,000 = (D) - (C) = (C)(D);
50,000 = (L);
8,000 = 5,000 + 1,000 + 1,000 + 1,000 = (V) + M + M + M = (V)MMM;
100 = C;
10 = X;
2 = 1 + 1 = I + I = II;
3. Wrap up the Roman number.
Put all the components together, construct the Roman number.
Substitute the Roman numerals calculated or listed above for each of the (place value) subgroups of the (Hindu-Arabic) number:
458,112 =
400,000 + 50,000 + 8,000 + 100 + 10 + 2 =
(C)(D) + (L) + (V)MMM + C + X + II =
(C)(D)(L)(V)MMMCXII;
(C)(D)(L)(V)MMMCXII is a group of numerals written in both additive and subtractive notation.
The final answer:
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: