Today’s Wonder of the Day was inspired by Samuel. Samuel Wonders, “How do roman numerals work?” Thanks for WONDERing with us, Samuel!
When you first learn to tell time, one of the things that can be confusing is a clock that has letters instead of numbers on it. What's up with that? Wouldn't it be easier if all clocks were digital? And what do those letters mean anyway?
The letters on those clocks are actually numbers! Well…sort of. We call them Roman numerals. Instead of using numbers like we're familiar with (1, 2, 3, etc.) — which are called Arabic numerals — the ancient Romans developed a numeric system which uses letters of the alphabet.
Here is the basic set of Roman numerals and what they represent:
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1,000
The rules for Roman numerals are a bit different than the rules for Arabic numerals. For example, Roman numerals don't have a place value like Arabic numerals do. If you put a “1" after a “5" using Arabic numerals, you have “51."
Using Roman numerals, though, “51" isn't represented by an “I" after a “V." Instead, it's represented by LI (L = 50 + I = 1). This is because Roman numerals use an additive (or subtractive) system to add or subtract value from the basic Roman numerals listed above.
Here are the basic rules you need to know to read and write with Roman numerals:
- A letter repeats its value as many times as it's used, but it can only be repeated three times. For example, XXX = 30.
- If one or more letters come after a letter of greater value, their values are added. For example, VII = 7 (5 + 1 + 1).
- If a letter comes before a letter of greater value, its value is subtracted. For example, IX = 9 (10 – 1 = 9). This rule has a few conditions: only subtract powers of 10 (I, X, or C — not V or L); only subtract one number from another; and don't subtract a number from another number that's more than 10 times greater.
- A letter with a bar over it has a value 1,000 times greater than usual. For example, V = 5, but V with a bar over it = 5,000.
In addition to certain clocks, you'll also often see Roman numerals used in the credits of movies to indicate the year of release. For example, if you go to the theater to see a new movie in 2018, you may see the letters MMXVIII instead of the Arabic numerals 2018.