Roman Numerals

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.

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

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:

1. 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.

2. When a letter is repeated multiple times, it gets added. 

Example: MMM = M + M + M = 1000 + 1000 + 1000 = 3000

3. 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.

4. Some symbols, like V, L, and D, can never be repeated.

5. If a smaller value symbol comes after a bigger one, you add them together. 

Example: VI = V + I = 5 + 1 = 6.

6. But if a smaller symbol comes before a bigger one, you subtract it. 

Example: IX = X - I = 10 - 1 = 9.

7. A numeral can only be subtracted once from another numeral (no repeat subtractions like IIX for 7).

8. 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.

1. There is no letter to denote Zero.

2. These are used for specific letters to represent numbers up to 5000, but they don't extend beyond that.

3. 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.

4. 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.

1. 69

2. 1984

3. 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

• Roman Numerals to Numbers

• Roman Numerals Conversion

• Roman Numbers From 1 to 500

• XXXVII Roman Numeral - Conversion, Rules and Uses

• Roman Numbers Addition

• How to Write the Roman Number 96?

• Roman Numbers Puzzle