Roman numerals are a system of numerical notations used by the Romans. It was the standard number system used by the Romans and other ancient Europeans. Rome being the world leader at the time were leaders in trade and commerce and as such they created a system where they could calculate their everyday finances. Also, being a modernize society in their era there was a demand and need to improve their architect capabilities in building roads, bridges etc; as they expanded and their society became more sophisticated. Thus, a numerical system was developed which resulted in the development of their mathematical skills to build a civil society that had buildings such as the Colosseum, Constantine's Arch, Pantheon and Roman Baths. Labels: Mathematics
Roman numerals are used today as a formality or just to add a classic style and elegance to ones work depending on ones taste or fashion.
After reading this article you should be able to:
Arabic numerals (also called Hindu numerals or Indian numerals or Western numerals ) are the most common set of symbols used to represent numbers and is also the one we use today. Arabic numerals is made up of the characters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 from which all the other sets of numbers are derived from to form our present number system.
Roman numerals unlike Arabic numerals which we use today didn't have a symbol for zero. Thus, a roman numeral can sometimes be read based on subtraction within its numbers rather than addition. This will be demonstrated further below. The Romans Numerals however had two flaws 1) it had no zero (0) in its numerical system 2) there were no single method for one to count above several thousand units. The limit was 4,999. To compensate for this, lines were often placed over numerals to indicate multiples of their value. This was however taken care of several years after, with the introduction and adoption of Arabic numerals.
Roman numerals spread in many countries during that era and thus there were different ways of writing the numbers during the centuries. For example, four (4) was written as IIII which was changed to IV. This became the universal numerical symbol of modern times. This used the subtraction notation method which will be demonstrated below. These rules here are however the standard used today.
Reading and writing Roman numerals
Step 1: Learn the meanings of the letters used in ancient Rome to represent numbers
The Roman letters I, V, X, L, C, D, and M, representing respectively the numbers 1, 5, 10, 50, 100, 500, and 1000, used by the ancient Romans. In other words; I = 1; V = 5; X = 10; L = 50; C = 100; D = 500; M = 1000.
The numbers one through ten (1-10) are written:
I = 1, II = 2, III = 3, IV = 4, V = 5, VI = 6, VII = 7, VIII = 8, IX = 9, and X = 10.
Step 2 : Symbol Duplication
A Roman letter repeated once, twice or thrice repeats its value that many times.
(XX = 20, CCC= 300, MMMM = 4000 etc.)
The Roman symbols V, L and D are not duplicated. This is due to the fact that their combined values can be expressed by other numerical symbols. For example, VV = 10 can also be written as X = 10. Thus, VV = 10 = X and therefore these three Romans number/symbols should not be doubled. Only powers of ten (X, I, C, M) can be repeated. No Roman Numeral must be repeated more than three times in a row. A common ancient Romans exception was IIII = 4 This is because IV is the first two letters of IVPITER, the main god of the Romans and thus it was not appropriate to use. However, this is now usually expressed by subordinate subtraction - IV. Today you may notice that some clocks still may use IIII instead of IV.
Step 3 : Simple Addition Rule
If a smaller Roman letter comes AFTER a larger letter, then add the value of the two characters together. In other words, if you put a small number (Roman letter) to the right of a large number (Roman letter) of greater value , then you add them.
XV means 10+5 =15 thus, XV=15
LXXV means 50+10+10+5 = 75 thus, LXXV= 75
MCC means 1000+100+100 = 1200 thus, MCC = 1200
CLXVI means 100+50+10+5+1= 166 thus, CLXVI= 166
Step 4 : Subordinate Subtraction
If a smaller number (roman letter) comes BEFORE a larger number (Roman letter), then subtract the value of the smaller from the value of the larger number/letter. That is, if a small number is placed to the left of a large number, then you subtract the small one from the big one. The result is then added to the rest of the letters.
Here are some more rules for subtraction.
(a) only subtract powers of ten i.e. I, X, and C. The subtraction of V or L are NOT allowed;
(b) only subtract one number from another;
(c) do not subtract a number from one that is more than 10 times greater. In other words, you can subtract 1 from 10 [IX] but not from 20 because there is no such number as IXX.
(d) If another letter follows the larger one, it must be smaller than the number preceding the larger one.
IX means 10 - 1 = 9 thus, IX =9
XL means 50 - 10 = 40 thus, XL = 40
CM means 1000-100= 900 thus, CM = 900
XLIX means (50 - 10) + (10 - 1) = 40+ 9 = 49 thus, XLIX= 49
XCIX means (100 - 10) + (10 - 1) = 90 + 9 = 99 thus, XCIX = 99
XLIII means (50 - 10) + 1 + 1 + 1 = 40+3 = 43 thus, XLIII = 43
In order to prevent duplication mistakes in their calculation of using their numeric system, it was necessary that certain numbers (compound numerals) must be written using subordinate subtraction. This preceding rule was put in place by their accountant (Tabularius - 'the worker of tables').
It is also important to note that subordinate subtraction was hardly ever done with duplicated Roman letters. For example, the Roman letters (numbers) IIX and CCD are both syntactically correct, but would more properly be represented by VIII and CCC respectively.
Step 5 : Higher Roman Numbers
For very large numbers (five thousand and above), a line (-) drawn over a numeral (letter) indicates that its value was to be multiplied by 1000.
V with a bar over it would be 5000 (five thousand)
X with a bar over it would be 10,000 (ten thousand)
L with a bar over it would be 50,000 (fifty thousand)
C with a bar over it would be 100,000 (one hundred thousand)
D with a bar over it would be 500,000 (five hundred thousand)
M with a bar over it would be1,000,000 (one million)
Thus, let say XV = 15,
then X (with a line on top) V (with a line on top) = 15,000
Due to the fact that barred letters are hard to write in HTML format, this example is shown with non-barred letters with the written explanation.
Also , notice that the Roman number "I" was not barred since I-bar equals "M." that is, I * 1000 = M
If lines were drawn on the top (-) and both sides (|) of a numeral, its value was multiplied by a hundred thousand. ( * 100,000)
|V| = 500,000 (five hundred thousand) and
|X| = 1,000,000 ( one million or ten hundred-thousands)
Tip: Converting from Arabic numerals to Roman numerals
When converting to Roman numerals, convert each digit separately. For example, for 752 convert 700, 50, and 2 to give CCCM, L. This will indicate wherever a subordinate symbol follows one of higher value. After this, the results combined to give the final figure.
Note: Roman Numerals are written in capital letters. This is because they did not have lower-case letters. So, remember to write it in capital letters.
To master this topic read this article twice making sure you understand it then get some practice by visiting the sites below. After this you should attain this article/lesson objectives and thus, you should be able to read and write Roman Numerals. Have fun!!
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