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# Roman Numerals

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Last updated date: 11th Sep 2024
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## Decoding Roman Numerals - Ancient Numeric System

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 Numbers I V X L C D M Numbers Digits 1 5 10 50 100 500 1000

### 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.

 Number RomanNumeral Number RomanNumeral Number RomanNumeral Number RomanNumeral Number RomanNumeral 1 I 21 XXI 41 XLI 61 LXI 81 LXXXI 2 II 22 XXII 42 XLII 62 LXII 82 LXXXII 3 III 23 XXIII 43 XLIII 63 LXIII 83 LXXXIII 4 IV 24 XXIV 44 XLIV 64 LXIV 84 LXXXIV 5 V 25 XXV 45 XLV 65 LXV 85 LXXXV 6 VI 26 XXVI 46 XLVI 66 LXVI 86 LXXXVI 7 VII 27 XXVII 47 XLVII 67 LXVII 87 LXXXVII 8 VIII 28 XXVIII 48 XLVIII 68 LXVIII 88 LXXXVIII 9 IX 29 XXIX 49 XLIX 69 LXIX 89 LXXXIX 10 X 30 XXX 50 L 70 LXX 90 XC 11 XI 31 XXXI 51 LI 71 LXXI 91 XCI 12 XII 32 XXXII 52 LII 72 LXXII 92 XCII 13 XIII 33 XXXIII 53 LIII 73 LXXIII 93 XCIII 14 XIV 34 XXXIV 54 LIV 74 LXXIV 94 XCIV 15 XV 35 XXXV 55 LV 75 LXXV 95 XCV 16 XVI 36 XXXVI 56 LVI 76 LXXVI 96 XCVI 17 XVII 37 XXXVII 57 LVII 77 LXXVII 97 XCVII 18 XVIII 38 XXXVIII 58 LVIII 78 LXXVIII 98 XCVIII 19 XIX 39 XXXIX 59 LIX 79 LXXIX 99 XCIX 20 XX 40 XL 60 LX 80 LXXX 100 C

### 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.

 Number Roman Numerals Evaluation 100 C 100 200 CC 100 + 100 300 CCC 100 + 100 + 100 400 CD 500 – 100 500 D 500 600 DC 500 + 100 700 DCC 500 + 100 + 100 800 DCCC 500 + 100 + 100 + 100 900 CM 1000 – 100 1000 M 1000

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.

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

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

1. 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.

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

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

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

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

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

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

2. 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.

 5000 10,000 50,000 100,000 500,000 1,000,000 $\overline{V}$ $\overline{X}$ $\overline{L}$ $\overline{C}$ $\overline{D}$ $\overline{M}$

### 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.

 Numbers Roman Numeral Numbers Roman Numeral 1 I 850 DCCCL 5 V 900 CM 10 X 950 CML 15 XV 1000 M 20 XX 1050 ML 25 XXV 1100 MC 30 XXX 1150 MCL 35 XXXV 1200 MCC 45 XLV 1250 MCCL 40 XL 1300 MCCC 50 L 1350 MCCCL 55 LV 1400 MCD 60 LX 1450 MCDL 65 LXV 1500 MD 70 LXX 1600 MDC 75 LXXV 1700 MDCC 80 LXXX 1800 MDCCC 85 LXXXV 1900 MCM 95 XCV 2000 MM 90 XC 2500 MMD 100 C 3000 MMM 150 CL 3500 MMMD 200 CC 4000 MV̅ 250 CCL 4500 MV̅D 300 CCC 5000 V̅ 350 CCCL 5500 V̅D 400 CD 6000 V̅M 450 CDL 6500 V̅MD 500 D 7000 V̅MM 550 DL 7500 V̅MMD 600 DC 8000 V̅MMM 650 DCL 8500 V̅MMMD 700 DCC 9000 MX̅ 750 DCCL 9500 MX̅D 800 DCCC 10000 X̅

### Roman Numerals from 1000 to 10000

 Numbers Roman Numeral 1000 M 2000 MM 3000 MMM 4000 MV̅ 5000 V̅ 6000 V̅M 7000 V̅MM 8000 V̅MMM 9000 MX̅ 10000 X̅

### 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.

 Value Roman Number Instead of(Do not follow this rule) 4 IV IIII 9 IX VIIII 40 XL XXXX 90 XC LXXXX 400 CD CCCC 900 CM DCCCC

## 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?

## FAQs on Roman Numerals

1. How would you count to 100 using Roman Numerals?

In the Roman numeric system, the letter I denotes the value of 1, and the letter V denotes the value of 5. So, when you start counting, the numbers go till 49 after which it has become very bulky as the number already consists of 4 Xs. So, the symbol for the letter 50 is denoted by “L”, the counting once again starts and goes till 99 after which the number once again becomes very bulky, hence the symbol for the number 100 is denoted by the letter c.

2. How can we do calculations using the Roman Numeric system?

The Roman Numerals are very distinctive in use. All of us can use them in calculation yet they create complications in advanced mathematics calculation and a very simple reason behind that is there is no concept of zero. Although subtraction and addition are easy to calculate, you cannot do multiplication and division.

The rule for the Addition of numbers - We must ignore the subtractive principle while we add the numerals. Let’s take one example.

Rules for the subtraction of numbers - We must not think subtraction rules are different from addition. While doing subtraction we need to avoid the subtraction rule too.

3. What is the utilization of the Roman Numeric system?

The Roman Numeric system is still widely used and has many uses, some of them are:

• At the international level, Events like the Olympics, Wrestlemania, Superbowl, etc use the Roman Numerals to create an impact on the viewers.

• Many movies use Roman numerals in their titles.

• Many Kings of medieval and ancient times has roman numerals in their names

• Batches and clubs in colleges use roman numerals to create titles, souvenirs, etc.

4. What are the failures of the Roman Numeric System?

Although the Roman numerals still have wide prevalence and significance in modern times, there are still many failures of the Roman numeric system because of which it became extinct from the academic disciplines of mathematics. These are:

• The absence of the concept of zero.

• The inability to conduct multiplication and division in this system.

• The problem with denoting large numbers

• Roman numerals are good only for denoting very small numbers and complex mathematical concepts like continuity cannot be explained using the roman numerals.

5. What is an abacus?

The abacus, which is also known as a counting frame, is a calculating tool that has been in use since ancient times and was helpful for people to do mathematical calculations once upon a time. It was used in Eastern Europe, Russia, China, and Italy centuries before the Indo-Arabic numeric system was introduced. The modern-day applications of the abacus have been very limited with this mostly being used as a toy for children during their early days from which they can learn about the basic concepts of mathematics.

6. How do we write 100 in Roman?

In Roman numerals, 100 is represented by C.

7. How to write 1 in Roman numerals?

1 is represented as I

8. How to write 2 in Roman numerals?

2 is represented as II

9. How to write 3 in Roman numerals?

3 is represented as III

10. How to write 4 in Roman numerals?

4 is represented as IV

11. How to write 5 in Roman numerals?

5 is represented as V

12. How to write 6 in Roman numerals?

6 is represented as VI

13. How to write 7 in Roman numerals?

7 is represented as VII

14. How to write 8 in Roman numerals?

8 is represented as VIII

15. How to write 9 in Roman numerals?

9 is represented as IX

16. How to write 10 in Roman numerals?

10 is represented as X

17. How to write 11 in Roman numerals?

11 is represented as XI

18. How to write 12 in Roman numerals?

12 is represented as XII

19. What is the use of Roman numerals?

We use them to label things, like the order or position of something or someone. For instance "Prince Charles III," where III represents the third. Also, schools often have classes labeled from Class 1 to Class 10, as I for 1st and X for 10th.

20. How many twin prime numbers are there between Roman Numerals 1-100?

Twin prime numbers are special because they are prime numbers that are only 2 apart. For example, 3 and 5 are twin primes because they're both prime and only 2 numbers away from each other. In the range of numbers from 1 to 100, we find 8 pairs of these special twin primes:

3 and 5

5 and 7

11 and 13

17 and 19

29 and 31

41 and 43

59 and 61

71 and 73

21. Find the sum of XXV XXV XIII XIV Roman numerals

The sum of the XXV, XXV, XIII, and XIV is 77.

XXV = 25

XXV = 25

XIII = 13

XIV = 14

25 + 25 + 13 + 14 = 77

22. What is the Roman figure of 1 to 5000?

Roman numerals are symbols like I, V, X, L, C, D, M that stand for numbers. You can use these symbols to write numbers up to 5000. Check the Vedantu page for the list of Roman numerals from 1 to 5000.

1: I

2: II

3: III

4: IV

5: V

6: VI

7: VII

8: VIII

9: IX

10: X

...

50: L

100: C

500: D

1000: M

5000: $\bar{V}$

23. What is the Roman number A to Z?

Roman numerals are not based on letters A to Z. They use specific symbols (I, V, X, L, C, D, M) to represent numbers. For example, 2019 is written as MMXIX.

24. What is XL in Roman?

XL is 40. X represents 10, and L represents 50. Since L is greater than X, XL represents 50 minus 10 (subtraction is allowed in certain cases with Roman numerals).

25. What does MMXX mean?

MMXX is 2020. MM represents 2000, and XX represents 20.

26. What is 13 no in Roman?

13 is written as XIII. X represents 10, and III represents 3.

27. What is MCMXC in years?

MCMXC represents the year 1990.

M = 1000

CM = 900 (C = 100, M = 1000, but since C is placed before M, it subtracts 100 from 1000)

XC = 90 (X = 10, C = 100, again C before X subtracts 100 from X)

28. What year is MMX?

MMX = MM + X = 2000 + 10 = 2010

MMX represents the year 2010.

29.What number is L?

L is the Roman numeral for 50.

30. What year is MCMX?

MCMX represents the year 1910.

M = 1000

CM = 900

X = 10

31. What does ix mean?

IX represents 9. I represent 1, and X represents 10. Since I is placed before X, it subtracts 1 from 10.