# Roman numerals Subtractive VS Additive

What is the Difference between Additive notation and Subtractive notation in Roman numerals?

correct me if im wrong but this is an example of Additive: XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33

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Yes, that’s an example of additive notation. IX $=10-1=9$ is an example of subtractive notation, as is XC $=100-10=90$. Roman numerals were originally entirely additive; the subtractive notation was a later development. – Brian M. Scott May 23 '12 at 6:51
Thanks for that you made it really clear :) – Daniel D C May 23 '12 at 6:52
@BrianM.Scott what would you say is the subtractive notation of my example though? – Daniel D C May 23 '12 at 6:56
There isn’t one: the subtractive notation is used only when an amount written with a single letter is being subtracted. One doesn’t write IIV, meaning $5-2$, for $3$, and similarly, one doesn’t write XXXIIV, XXLIII, or XXLIIV, meaning $30+5-2,50-20+3$, and $50-20+5-2$, for $33$. – Brian M. Scott May 23 '12 at 7:00
Just as an example for subtractive notation, 1999 is not generally written "IM", as might be supposed, but rather "MCMXCIX". – JL344 Jul 2 '12 at 6:13

## 1 Answer

IIII and IV are both used for 4. IIII is additive; IV is subtractive.

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Actually four repetitions of the same symbol became common during the Middle Ages. During the golden age of the Roman civilization (I century BC) only up to three repetitions were allowed by "proper grammar", so to speak. – Andy Jul 2 '12 at 8:15