Roman Numerals: Types, Rules, Chart, Examples, Method to Write

Roman numerals indicate a number system that originated in ancient Rome and was used for counting and performing other day-to-day transactions. It remained the standard numeral system throughout Europe until the late middle ages. The Roman Numerals were represented by using letters from the Latin alphabet. The system of Roman Numerals used seven different letters as symbols to represent numbers. Roman numerals are used even today in several contexts such as hour marks on a clock, to denote the names of Popes and Kings, etc. In this article, we have given a detailed description of how to write and interpret Roman numerals. Moreover, we will discuss several tips and tricks that will make Roman Numerals easy to understand and remember. Read on for more information.

Introduction to Roman Numerals

Roman numerals are a particluar type of number system used for representing fixed integer values. Modern Roman numerals have seven letters to represent different numerical values. These are I, V, X, L, C, D, and M and their respective integer values are 1, 5, 10, 50, 100, 500, and 1000 respectively.

History of Roman Numerals

The Roman numerals originated in ancient Rome, as the name suggests. However, there was no universally accepted standard for Roman numerals as the usage in ancient Rome got discontinued and became thoroughly disordered in medieval times. This system originated because the ancient Romans understood that numbers after 10 were very hard to count on one’s fingers. So, they had to create a standardized system that could be used for commerce and communications. The Roman Numeral system was widely used throughout Europe as the standard numeral system until the late middle ages.

Types of Number Systems

We use different types of number systems that use different symbols for expressing numbers. We commonly use the Hindu-Arabic numeral system. In this system, we use digits to represent the number system.

Types of Roman Numerals or Roman Letters

Roman numerals number system uses seven different letters as symbols to represent numbers. They are:
\(I,\,V,\,X,\,L,\,C,\,D,\,M\)

We generally read the above as letters. But how about numbers?

Let us learn how the above letters can be read as a number.

\(\begin{array}{l} I \to 1\\ V \to 5\\ X \to 10\\ L \to 50\\ C \to 100\\ D \to 500\\ M \to 1000 \end{array}\)

Now, what about the other numbers like \(2,\,3,\,4,\,6,\,….\)

We need to follow certain rules to write the other numbers using letters as explained below.

Different Rules for Writing Numbers in Roman Numerals

Rule 1: (a) The roman numerals \(I,\,X\) and \(C\) can repeat up to three times in sequence to form the numbers. In other words, if a letter comes after itself, then we can say it is added.

Example: \(2\) can be written as \(II,\,20\) can be written as \(XX.\,200\) can be written as \(CC.\)

\( \Rightarrow I = 1,\,II = 1 + 1 = 2,\,III = 1 + 1 + 1 = 3\)
\(X = 10,\,XX = 10 + 10 = 20,\,XXX = 10 + 10 + 10 = 30\)
\(C = 100,\,CC = 100 + 100 = 200,\,CCC = 100 + 100 + 100 = 300\)

(b) No letter is repeated in sequence more than thrice, i.e., \(I,\,X\) and \(C\) cannot be repeated more than thrice.

(c) The letters \(V,\,L\) and \(D\) are not repeated. The repetition of \(V,\,L\) and \(D\) is invalid in the generation of numbers.

Rule 2: When a letter of lower value is written to the right or after a letter of higher value, the values of all the letters are added.

Example:

\(6 = 5 + 1 = VI,\,7 = 5 + 2 = VII,\,8 = 5 + 3 = VIII\)
\(11 = 10 + 1 = XI,\,12 = 10 + 2 = XII,\,13 = 10 + 3 = XIII\)
\(15 = 10 + 5 = XV,\,16 = 10 + 5 + 1 = XVI,\,17 = 10 + 5 + 2 = XVII\)
\(60 = 50 + 10 = LX,\,65 = 50 + 10 + 5 = LXV,\,70 = 50 + 20 = LXX\)

Rule 3: When a letter of lower value is written to the left or before a letter of higher value, then the value of the lower letter is subtracted from the value of the digit of the higher letter.

Example:
\(\begin{array}{l} 4 = 5 – 1 = IV\\
9 = 10 – 1 = IX\\
14 = 10 + \left( {5 – 1} \right) = XIV\\
40 = 50 – 10 = XL\\
19 = 10 + \left( {10 – 1} \right) = XIX\\
29 = 10 + 10 + \left( {10 – 1} \right) = XXIX\\
45 = \left( {50 – 10} \right) + 5 = XLV\\
159 = 100 + 50 + \left( {10 – 1} \right) = CLIX
\end{array}\)

Also, remember \(V\) is never written to the left of \(X.\)

Rule 4: (a) If we must write the numbers after \(10\) we should write the number \(10\) or groups of number \(10\) and then number \(1\) or \(5\) as the case may be. Then these numbers are used to change to the corresponding Roman numerals.

Example:
\(\begin{array}{l} 13 = 10 + 3 = 10 + 1 + 1 + 1 = XIII\\
20 = 10 + 10 = XX\\
23 = 10 + 10 + 1 + 1 + 1 = XXIII\\
38 = 10 + 10 + 10 + 5 + 1 + 1 + 1 = XXXVIII\\
39 = 10 + 10 + 10 + XXXIX
\end{array}\)

(b) According to this pattern, numbers greater than number \(40\) are also formed.

Example:
\(\begin{array}{l} 42 = \left( {50 – 10} \right) + 1 + 1 = 40 + 1 + 1 = XLII\\
57 = 50 + 5 + 1 + 1 = LVII
\end{array}\)

Rule 5: If a horizontal line is drawn over the symbols or letters of Roman numerals, then the value of the numbers becomes \(1000\) times.

Example:
The value of \(25 = XXV\) but \(\overline {XXV} = 25000\)

How to Write Roman Numerals from 1 to 100?

Following is the list of Roman numerals from \(1\) to \(100.\)

Roman Numerals Chart from 1 to 1000

Solved Examples – Roman Numerals

Q.1. Write the numbers for the following Roman numerals.
\(a.\,VII\, b.IX\, c.XIX\, d.XXVII\)
Ans: The numbers for the above roman numerals are:
a. \(VII = 7\)
b. \(IX = 9\)
c. \(XIX = 19\)
d. \(XXVII = 27\)

Q.2. Add the below roman numerals and write the answer in the Roman numerals.
a. \(XXIX + XLII\)
b. \(XCV + XXV\)
Ans: a. \(XXIX + XLII\)
We know that \(XXIX = 29\) and \(XLII = 42\)
So, \(29 + 42 = 71\)
Therefore, \(XXIX + XLII = LXXI\)
b. \(XCV + XXV\)
We know that \(XCV = 95\) and \(XXV = 25\)
So, \(95 + 25 = 120\)
Therefore, \(XCV + XXV = CXX\)

Q.3. Subtract the below roman numerals and write the answer in the Roman numerals.
a. \(XCV – XIV\)
b. \(XXXVIII – X\)
Ans: a. \(XCV + XIV\)
We know that \(XCV = 95\) and \(XIV = 14\)
So, \(95 -14 = 81\)
Therefore, \(XCV – XIV = LXXXI\)
b. \(XXXVIII – X\)
We know that \(XXXVIII = 38\) and \(X = 10\)
So, \(38 + 10 = 28\)
Therefore, \(XXXVIII – X = XXVIII\)

Q.4. Divide the below roman numerals and write the answer in the same.
a. \(LXIII \div VII\)
b. \(LXVI \div XI\)
Ans: a. We know that \(LXIII = 63\) and \(VII = 7\)
So, \(63 \div 7 = 9\)
Therefore, \(LXIII \div VII = IX\)
b. We know that \(LXVI = 66\) and \(XI = 11\)
So, \(66 \div 11 = 6\)
Therefore, \(LXVI \div XI = VI\)

Q.5. Convert the given numbers to Roman numerals.
\(1,\,2,\,5,\,7,\,10,\,13,\,15,\,16,\,18,\,27,\,38,\,39,\,43,\,62,\,218,\,546\)
Ans: \(\begin{array}{l} 1 = I\\
2 = II\\
5 = V\\
7 = VII\\
10 = X\\
13 = XIII\\
15 = XV\\
16 = XVI\\
18 = XVIII\\
27 = XXVII\\
38 = XXXVIII\\
39 = XXXIX\\
43 = XLIII\\
62 = LXII\\
218 = CCXVIII\\
546 = DLXVI \end{array}\)

Q.6. Convert the given Roman numerals to numbers.
\(VIII,\,XVII,\,XXV,\,XXXVI,\,XLIII,\,XLIX,\,LIII,\,LVII,\,CXXI,\,CXLIII,\,CLIV\)
Ans: \(\begin{array}{l} VIII = 8\\
XVII = 17\\
XXV = 25\\
XXXVI = 36\\
XLIII = 43\\
XLIX = 49\\
LIII = 53\\
LVII = 57\\
CXXIV = 124\\
CXLIII = 143\\
CLIV = 154 \end{array}\)

Summary

The Roman numeral was a common method of counting for trade and communication. The Roman numerals number system used seven different letters as symbols to represent numbers. From the above article, we learn about Roman numerals and the history of Roman numerals. We learnt how to form the numbers using the different rules of writing the Roman numerals. Finally, we can write the required numbers in the Roman numerals format and convert the Roman numerals into numbers. We learnt how to write 1 to 100 in Roman notation.

Frequently Asked Questions (FAQs) – Roman Numerals

Here we have provided the answers to some of the most commonly asked questions about Roman Numerals:

We hope you find this article on Roman Numerals helpful. In case of any queries, you can reach back to us in the comments section, and we will try to solve them.