Roman Arithmetic

...basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large numbers, simply pile all the letters together, arrange them in descending order, and there’s your sum. CLXVI plus CLXVI? CCLLXXVVII, or CCCXXXII. And one of the advantages of the Roman system is that you don’t need to memorize multiplication tables. What’s VI times VI? Six Vs and six Is, which converts to three Xs, a V, and an I: XXXVI.

You can do all this because of the limitation Leonard pointed out above. Roman numerals don’t have what’s called place value, or positional value, the way digits in our system do. The value represented by the Arabic numeral 5 changes depending on its placement within a figure: it can mean five units, or five tens, or five hundreds. But to a Roman, V always meant just plain five, regardless of position. And before you chime in with “What about in IV?” keep in mind that the Roman numerals we use aren’t necessarily the ones the Romans used. Subtractive notation—expressing a value as the difference between a larger number and a smaller one set to its left—was rare in classical Rome and didn’t take off until the middle ages; the Romans greatly preferred the simpler IIII to IV, XXXX to XL, and so on. (The IIII-for-4 notation survives today on the faces of clocks.)