Roman Numerals (Math Quiz)

Roman numerals
Clock face with Roman numerals

If you are familiar with the rules and theory of the Roman numeral system you may skip the theory part and head down to take the math quiz and test your knowledge.


As the name says, Roman numerals were used by the Romans, and they continued to be use till the 14th century, when they were gradually replaced by the more convenient decimal system.
The Roman numeral system is based on seven symbols:

Symbol I V X L C D M
Wert 1 5 10 50 100 500 1000

Numbers are formed by combining symbols together. The following rules apply:


1. Symbols are placed from left to right in sequence of value, i.e. the largest symbol is placed to the very left, and the smallest to the very right. Their combined value is obtained by adding up the values of the individual symbols.
This is the general underlying rule, however (and this makes it tricky!!) one must avoid repeating four symbols in succession (e.g. writing “IIII” to express “4” ist not permitted). Therefore these additional rules apply:

2. If a symbol with a lower value is placed before (i.e. to the left of) a certain symbol, then the value of the symbol with the lower value shall be subtracted from the value of the symbol with the higher value. In doing so only one symbol with a lower value may preceed a symbol with a higher value.

Example 1:
CX = 100 + 10 = 110
XC = 100 – 10 = 90

Example 2:
CXX = 100 + 10 +10 = 120
(XXC to express 80 is not permitted!!)
Instead: 80 = LXXX = 50 + 10 + 10 + 10

Example 3:
998 = CMXCVIII (und not IIM)

3. The symbols I, X, C, and M may only be repeated up to three times in succession.

4. V, L, and D must not preceed a symbol with a higher value, and they also may not be repeated two (or more) times in succession.

Example 4:
(LD to express 450 is not permitted!!)
Instead: 450 = CDL = -100 + 500 + 50

Roman numerals are still used today in several niche contexts, like in the names of Popes and monarchs, the hour marks on clocks and timepieces (see the featured image of this article), some sport events (e.g. the Summer and Winter Olympics, and the Super Bowl), etc. More examples of modern usage can be found here.


Click on the button to take the test!


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