Roman Numerals Chart, Rules, and Practice Exercises
The Roman number System is one of the earliest number systems still in use today. Although the usage of these numbers has been limited to extremely particular uses, and the Indo-Arabic numeric system handles the majority of current-day operations, the Roman numeral system retains its position in the modern world. Rather than utilizing numerals (1, 2, 3, etc.), they utilized letters such as I, II, III, IV, etc. These letters represented different values. For example, V denoted 5, X represented 10, and so on. They also had techniques to add and subtract with these letters. Roman numerals are still used today in various contexts, such as class names (Class I, Class II, …., Class X … etc.).
What is Roman Numerals?
Roman numerals are an old numbering system that is still widely used today. These use alphabets for expressing fixed positive integers. The Roman numeral I, II, III, IV, V, VI, VII, VIII, IX, and X represent the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
After 10, they add more letters. XI is 11, XII is 12, and so on up to XX for 20. The table below lists the most popular Roman numerals used to represent fundamental numbers.
Roman Numerals Chart (1 to 1000)
Here is a Roman numerals chart from 1 to 1000. It shows how to write numbers like 1, 2, 3, all the way up to 1000. It is simple to write any number in Roman numerals from 1 to 1000 with Roman numeral chart.
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Roman Numbers from 1 to 100
Learn Roman numbers from 1 to 100 with the provided chart. Converting between them can be difficult, This basic instruction will teach you how to write Roman numerals up to 100.
Roman Numbers from 1 to 100 Chart
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How to Write Roman Numbers from 1 to 100?
There are two ways to write Roman numerals 1-100 in simple terms:
First way: You take the number you want to write in Roman form and break it down into smaller parts. Then you use the letters that stand for those parts and put them together.
Example: Let's take 65.
From the Roman numbers 1 to 50
You take 50 - L, 10 - X, 5 - V
Put them together, 65 = 50 + 10 + 5 = L + X + V = LXV.
Second way: You look at the number in groups.
Example: For 65, 60 is written as 'LX', and 5 as 'V'. Put them together, you still get LXV.
You can use either of these methods.
Roman Numerals from 100 to 1000
Now, we are going to learn about bigger numbers, like hundreds and thousands. We will mix these with the ones you already know (from 1 to 100) to make even bigger numbers.
The table shows how we figure out and write Roman numbers to letters.
Using Roman Letters in Numerals
In English, we have 26 letters in the alphabet, but not all of them are used in Roman numerals. Out of the 26 letters, three are not used in Roman alphabet numerals: J, U, and W. So, 23 letters are used in Roman alphabet numerals. They are A, B, C, D, E, F, G, H, I, K, L, M, N, O, P, Q, R, S, T, V, X, Y, and Z. These letters are also called Roman symbols. For example, instead of writing the year 2024, you can write it as MMXXIV using Roman numerals.
How to Write Roman Numerals Correctly - Important Rules
If you want to write a number using Roman numbers, you have to follow some rules. Here they are:
When you see a Roman numeral symbol, its value is added to itself every time it's repeated.
Example: II means 2, XX means 20, and XXX means 30.
When a letter is repeated multiple times, it gets added.
Example: MMM = M + M + M = 1000 + 1000 + 1000 = 3000
You can not repeat a symbol more than three times.
Example: XXX means 30 which is valid, but you can not write XXXX for 40.
Some symbols, like V, L, and D, can never be repeated.
If a smaller value symbol comes after a bigger one, you add them together.
Example: VI = V + I = 5 + 1 = 6.
But if a smaller symbol comes before a bigger one, you subtract it.
Example: IX = X - I = 10 - 1 = 9.
A numeral can only be subtracted once from another numeral (no repeat subtractions like IIX for 7).
You can only subtract I from V and X, and X from L, C, and M.
Conversion of Roman Numerals to Numbers
Roman Numerals are very distinctive in use. Any of us can use them in calculation yet they create complications in advanced mathematics calculation and the very simple reason behind that is no place for Zero. Although subtraction and addition are easy to calculate you can’t do multiplication and division.
Rule 1: When symbols are together, add their values if the second one is bigger than the first.
Example:
VIII = 8 [5 (V) + 3 (III) = 8]
DCC = 700 [500 (D) + 100 (C) + 100 (C) = 700]
MCCC = 1300 [1000 (M) + 100 (C) + 100 (C) + 100 (C) = 1300]
Rule 2: If a symbol is before a bigger one, subtract its value.
Example:
IX = 9 [10 (X) – 1 (I) = 9]
XC = 90 [100 (C) – 10 (X) = 90]
CM = 900 [1000 – 100 (C) = 900]
Rule 3: Instead of writing 1000, use a bar on top of a symbol.
Roman Numbers from 1 to 10000
Learning Roman numbers 1 to 10000 can help students understand how to convert higher numbers beyond 1000 from the below table.
Roman Numerals from 1000 to 10000
Subtractive Rule of Roman Numerals
Understanding this rule allows you to write Roman numerals for numbers like 4, 9, 40, 90, 400, and 900 efficiently where X can be subtracted from L, C, and M.
Genesis of Roman Numerals - History
There were a variety of counting systems were used by our ancestors. The habitats of central Italy had developed their numeral system with vast varieties of symbols that were very different from the current Roman numeric symbols. There are primarily two types of theory prevalent in the world about the origin of Roman Numerals.
The first theory suggests that hand signals are used to display Roman Numerals and the equivalent amount of fingers signals the numbers ranging from 1 to 4 and when the thumb and fingers get separated this technique makes the shape of “V” to signal number 5.
While the second theory includes very interesting facts about tally sticks. The Tally sticks had been existed before Romans for many decades and had their existence till the 19th century in Europe. Hence, Several Roman Numbers were engraved on the top-notch of these tally sticks. We can understand this process with a simple example. IIIVI would be etched on the tally stick and when it got shortened it would look just like the Roman numeral of 6.
Failures of Roman Numerals
Roman Numerals are very creative and engaging. They have a vast variety to use, instead of that; they have numerous failures in the day to day life. Let’s discuss these failures in detail.
There is no letter to denote Zero.
These are used for specific letters to represent numbers up to 5000, but they don't extend beyond that.
These are still utilized in various contexts such as movie credits and architectural projects, yet many find them impractical for everyday use compared to our standard number system.
Roman Numerals seem very useful in denoting years or credits but while doing calculations they become very complicated.
Solved Examples on Roman Numerals
1. Convert the given numbers into the Roman numeral.
69
1984
1774
Solution:
a. For 69
To write a number like 69 it down into its parts that is 60 and 9.
On converting each part we get
69 = 60 + 9
69 = LX + IX
Thus, 69 = LXIX
Or
69 = 60 + 9
69 = [50 (L) + 10 (X)] + [10 (X) – 1 (I)]
69 = LX + IX
69 = LXIX
b. For 1984
Break the number 1984 into 1000, 900, 80 and 4
On converting each part we get
1000 = M
900 = CM
80 = LXXX
4 = IV
On Substituting,
1984 = 1000 + 900 + 80 + 4
1984 = M + CM + LXXX + IV
Hence, 1984 = MCMLXXXIV
c. For 1774
Break 1774 into 1000, 700, 70, 4
On converting each part we get
1000 = M
700 = DCC
70 = LXX
4 = IV
On Substituting,
1774 = 1000 + 700 + 70 + 4
1774 = M + DCC + LXX + IV
Hence, 1774 = MDCCLXXIV
2. Calculate the Roman number MXXII - LXX - LII.
Solution:
Given, MXXII – LXX – LII.
We know that MXXII = 1000 (M) + 22 (XXII) = 1022, LXX = 70 and LII = 50 (L) + 2 (II) = 52.
Now, substituting these numbers in the Roman numeral letters, we get;
MXXII – LXX – LII = 1022 – 70 – 52.
MXXII – LXX – LII = 900.
MXXII – LXX – LII = CM.
Hence, the number 900 (CM) in the Roman numeral.
3. Find the product of XVIII and LXX using Roman numerical
Solution:
We know that, XVIII = 10 + 8 = 18 and LXX = 70
By taking product we get, XVIII × LXX = 18 × 70 = 1260
1260 can be written as,
1260 = 1000 + 100 + 100 + 50 + 10
1260 = M + C + C + L + X
1260 = MCCLX
Hence the product of XVIII and LXX is MCCLX
4. Find the value of LXXVII - XIII
Solution:
LXXVII = 70 (LXX) + 7 (VII) = 77
XIII = 10 (X) + 3 (III) = 13.
Therefore, LXXVII - XIII = 77 - 13 = 64.
64 can be written as,
64 = 60 + 4
64 = LX + IV
64 = LXIV
5. Find the value of XCIII + (LXXIV - XLI) + XLIX
Solution:
By using Roman Numbers from 1 to 100, we get
XCIII = XC (90) + III (3) = 93
LXXIV = LXX (70) + IV (4) = 74
XLI = XL (40) I (1) = 41
XLIX = XL (40) IX (9) = 49
On substituting and simplifying the given equation, we get
XCIII + (LXXIV - XLI) + XLIX = 93 + (74 - 41) + 49 = 175
175 = 100 + 70 + 5 = C + LXX + V = CLXXV
6. How many perfect cubes are there in XXVII Roman numerals
First let us Convert XXVII to a decimal number,
XXVII = 20 + 7 = 27.
Let us now find perfect cubes less than 27:
Perfect cubes are integers that can be obtained by multiplying a number by itself three times. In this case, the perfect cubes less than 27 are 1 (1 x 1 x 1) and 8 (2 x 2 x 2).
Practice Questions
Convert 1108 into a Roman numeral.
Convert CXII into the number form.
What is the number form of the Roman numeral CMXXIII?
Related Links
FAQs on Roman Numerals Explained for Students
1. What are the basic symbols used to write Roman numerals?
The Roman numeral system is based on seven fundamental symbols, each with a specific value. Understanding these is the first step to reading and writing any Roman numeral. The primary symbols are:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
All other numbers are formed by combining these symbols according to a set of rules.
2. How does the subtractive principle work in Roman numerals, for example in IV or XL?
The subtractive principle is a key rule used to write numbers like 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD), and 900 (CM). It states that when a symbol of smaller value is placed before a symbol of greater value, its value is subtracted from the greater one. For instance, in 'IV', I (1) comes before V (5), so we calculate it as 5 - 1 = 4. Similarly, 'XL' is 50 - 10 = 40. This rule helps avoid repeating a symbol four times (e.g., IIII for 4 is less common than IV).
3. Can you perform mathematical calculations like addition and subtraction with Roman numerals?
Yes, simple addition and subtraction can be performed with Roman numerals, but it can be cumbersome. For addition, you combine the symbols and then simplify them (e.g., XII + V = 12 + 5 = 17, which is XVII). For subtraction, you convert the numbers, perform the operation, and then convert back. However, the system is not efficient for complex calculations like multiplication or division, primarily because it lacks a symbol for zero and a place-value system.
4. What is the importance of Roman numerals in the modern world?
Despite the Hindu-Arabic system being standard, Roman numerals still hold importance for stylistic and traditional reasons. Their primary modern uses include:
- Clock Faces: They add a classic, formal look to analogue clocks.
- Naming Conventions: Monarchs, popes, and ships are often numbered sequentially (e.g., Queen Elizabeth II, Super Bowl LV).
- Chapter and Volume Numbers: Books, outlines, and documents use them to number chapters or sections.
- Copyright Dates: Movies and TV shows often display the year of production in Roman numerals (e.g., MMXXIV for 2024).
5. What are the main limitations of the Roman numeral system compared to the Hindu-Arabic system we use today?
The Roman numeral system has several significant limitations, which is why the Hindu-Arabic system (0-9) is used globally for mathematics. The key failures are:
- No Concept of Zero: The absence of zero makes place-value notation and advanced arithmetic impossible.
- Difficulty in Calculation: Performing multiplication, division, or working with fractions is extremely complex and impractical.
- Writing Large Numbers: Representing very large numbers is bulky. For example, 3,888 is written as MMMDCCCLXXXVIII.
- No Place Value: The value of a symbol does not change based on its position in the same way it does in a number like '220', where each '2' has a different value.
6. How are large numbers, like those over 1,000, represented in Roman numerals?
To represent numbers in the thousands, the symbol M (1000) is repeated. For example, 3000 is written as MMM. For even larger numbers, a historical convention known as the 'vinculum' is used. This involves placing a bar over a numeral, which multiplies its value by 1,000. For instance:
- V̅ represents 5,000.
- X̅ represents 10,000.
- L̅ represents 50,000.
So, the number 7,000 could be written as V̅II.
7. Do Roman numerals use all the letters from A to Z?
No, this is a common misconception. The Roman numeral system does not use the entire alphabet. It is based on only seven specific Latin letters: I, V, X, L, C, D, and M. No other letters, such as A, B, E, or Z, have any numerical value in this system. The system works by combining only these seven symbols to represent all numbers.
8. Since Roman numerals don't have a symbol for zero, how did this affect their use in mathematics?
The absence of zero was a major drawback that severely limited the mathematical application of Roman numerals. Without a zero, there is no way to represent a null value or to have a place-value system, which is the foundation of modern arithmetic. This made it nearly impossible to perform complex operations like long division or multiplication efficiently. While sufficient for counting and basic record-keeping, this limitation prevented the system from being used for advanced fields like algebra or calculus, leading to its replacement by the Hindu-Arabic system.
9. What is the key difference in writing the number 99 as XCIX versus an incorrect form like IC?
The key difference lies in the rules of subtraction. While 'IC' might seem like a logical way to write 99 (100 - 1), the subtractive principle has restrictions. You can only subtract powers of ten (I, X, C) from the next two higher values (I from V and X; X from L and C; C from D and M). You cannot subtract I from C. The correct way to form 99 is to break it down into (90) + (9). 90 is written as XC (100 - 10), and 9 is written as IX (10 - 1). Combining them gives XCIX.
10. How can I read a complex Roman numeral like MCMXCIX correctly?
To read a complex Roman numeral, it's best to break it down into its components from left to right, looking for both additive and subtractive parts. Let's take MCMXCIX:
- M = 1000
- CM = 900 (C is before M, so 1000 - 100)
- XC = 90 (X is before C, so 100 - 10)
- IX = 9 (I is before X, so 10 - 1)
Now, add these values together: 1000 + 900 + 90 + 9 = 1999. This method of breaking the numeral into place-value-like chunks makes any number easy to read.
