# Roman Numerals

Here we will learn about Roman Numerals which are the special kind of numerical notations.

We have already learnt about the Indian and the International systems of numeration. There is another numeration system called the System of Roman Numeration. This is the oldest system of numeration, developed by the Romans and is still in common use.

REMEMBER: Roman numbers did not have '0' and so they did not have the concept of place values.

How to read and write roman numerals?

Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0.

Roman numeral system is one of the systems in which certain symbols are used to represent numbers. There are seven basic Roman numerals (Symbols).

The symbol of Roman Numerals and their values are:

Note: We also use K for 1000.

Romans used different combinations of symbols to write numbers using adding and subtraction.

For reading and writing numbers upto 50 we need only the first 4 symbols.

I V X L

The numerals used in the present number system (decimal system) are

0,        1,        2,        3,        4,        5,        6,        7,        8,        9.

These numerals were invented by Indians and later through the Arabs reached Europe. Hence this number system is termed as Hindu-Arabic Number System.

Early Romans developed a system of numerals. They are called Roman numerals. These are also commonly used in day-to-day life.

Sometimes the units of a book, different volumes of a book, class rooms in a school, the parts of a question, etc., are numbered in Roman numerals. On the dials of some clocks the hours are marked in Roman numerals.

Roman numerals are formed by using 7 symbols –

I,        V,        X,        L,        C,        D,        M.

The following table shows the Roman numerals and their corresponding values.

Roman Numerals

I

V

X

L

C

D

M

Value of the symbol in Hindu-Arabic numbers.

1

5

10

50

100

500

1000

This is not a place value system.

The numbers 2, 3, 4, 6, 7, 8 and 9 don’t have symbols in Roman System.

They are got by the method of addition or subtraction.

Rules for the First Five Symbols:

1: Multiplication Rule:

When a symbol is repeated in succession, we multiply the value of the numeral by the number of times it is repeated.

A symbol cannot be repeated more than three times in succession.

i.e., The symbol I, X, C and M can be repeated in succession up to 3 times only in writing a number.

For example:

II = 1 × 2 = 2

III = 1 × 3 = 3          or,  III = 1 + 1 + 1 = 3

XX = 10 × 2 = 20

XXX = 10 × 3 = 30    or,  XXX = 10 + 10 + 10 = 30

CCC = 100 × 3 = 300     or, CCC = 100 + 100 + 100 = 300

We cannot write 40 as XXXX.

The symbol cannot be repeated more than three times.

If a symbol is repeated at the most 3 times, its value is added as many times as it occurs, e.g., II = 2; XX = 20; XXX = 30, etc.

Writing a smaller number to the right of a larger number means the numbers have to be added.

i.e., If a symbol is written to the right of a greater number, we add its value to the value of the symbol on the left.

For example:

VI = 5 + 1 = 6

XI = 10 + 1 = 11

XII = 10 + 1 + 1 = 12

XV = 10 + 5 = 15

LXV = 50 + 10 + 5 = 65, etc.

Note: X can be repeated at the most 3 times.

3. Subtraction Rule:

Writing a smaller number to the left of a larger number means that the smaller number has to be subtracted from the larger number. The symbol I can be used for subtraction from V and X only. The symbol X can be subtracted only from L and C.

i.e., If a symbol is written to the left of a greater number, we subtract its value from the value of the symbol on the right.

For example:

IV = 5 - 1 = 4

IX = 10 - 1 = 9

XL = 50 - 10 = 40

The symbol V cannot be repeated or subtracted.

We do not repeat V twice to get 10. We already have a symbol for 10. So VV for writing 10 is not correct.

We do not subtract 5 from any symbol. VX is not correct.

Rule 4. The symbol V, L and D are not repeated to form a bigger number.

i.e., A symbol is not repeated more than three times and the symbols V, L, D are never repeated.

For Example: 10 = X but 10 ≠ VV, etc.

Rule 5. Symbols V, L and D are never subtracted,

For Example: 5 = V but 5 ≠ VX, etc.

Rule 6. While writing Roman numbers first write the largest numeral. Then put smaller numerals to the right (for addition) or left (for subtraction)

Note: The symbol V is never subtracted.

Rule 7. If X is written to the left of L and C, it is subtracted,

For Example: XL = 50 - 10 = 40,

XC = 100 - 10 =90.

Note: X can be subtracted from L and C only.

The following table gives the Roman numerals corresponding to the Hindu-Arabic numerals.

 Hindu-Arabic Numbers Roman Numbers 12345678910111213141516171819202122232425262728293034394045505559607580889095100 IIIIIIIVVVIVIIVIIIIXXXIXIIXIIIXIVXVXVIXVIIXVIIIXIXXXXXIXXIIXXIIIXXIVXXVXXVIXXVIIXXVIIIXXIXXXXXXXIVXXXIXXLXLVLLVLIXLXLXXVLXXXLXXXVIIIXCXCVC

A list of Roman Numerals and their value are given below:

Writing Numbers in Roman Numerals:

For example:

1. Write the Roman Numerals for 27. Break up the number into Tens and Ones.

27 = 20 + 7

Write the symbol for 20 (XX) and place the symbol for 7 (VII) after it.

27 convert roman numerals as XXVII

2. Write the Roman numeral number for 43.

43 = 40 + 3

Symbol for 40 XL

Symbol for 3 III

Roman Numerals for 43 is XLIII.

3. Write 45 in Roman numeral.

We cannot write 45 as VL, because V is never subtracted.

Hence 45 = (50 – 10) + 5

= (L – X) + V

= XLV

Note: V, L and D do not precede any bigger digit.

4. Write 39 in Roman numeral.

39 = 30 + 9

= (10 + 10 + 10) + (10 - 1)

= (X + X + X) + (X – I)

= XXXIX

5. Write the following in Roman numerals:

(i) 53

(ii) 45

(ii) 98

(iv) 587

Solution:

(i) 53 = 50 + 3 = L + III = LIII

(ii) 45 = 40 + 5 = XL + V = XIV

(It should not be written as 50 - 5 ,i.e.,VL)

(iii) 98 = 90 + 8 = XC + VIII = XCVIII

(It should not be written as 100 - 2, i.e., IIC)

(iv) 587 = 500 + 50 + 10 + 10 + 10 + 5 + 2 = DLXXXVII

Look out for a subtraction operation. Do the subtraction before adding the numbers.

For example:

1. XXIV

I = 1

V = 5

IV = 4

XX = 20

IV = 4

Hindu–Arabic numeral for XXIV is 24.

2. XIX

X = 10

IX = 9

Hindu–Arabic number for XIX = 19

3. XXXII

In this example no subtraction is needed.

XXX = 30

II = 2

Hindu – Arabic number for XXXII = 32

4. Express XIV in decimal system of numeration.

XIV = X – IV

= 10 + 4

= 14

5. Express XXXV in decimal system of numeration

XXXV = XXX + V

= X + X + X + V

= 10 + 10 + 10 + 5

= 35

6. Write the following in Hindu Arabic (Indian) numerals:

(i) LXIII;     (ii) XC;     (iii) XXXVI

Solution:

(i) LXIII = L + X + III = 50 + 10 + 3 = 63

(ii) XC = 100 - 10 = 90

(iii) XXXVI = XXX + VI = 30 + 6 = 36

Solved Examples on Roman Numerals:

1. Write the Hindu-Arabic numerals for the following:

(i) XXII

(ii) IX

(iii) XIV

(iv) XXXIX

Solution:

(i) XXII = 10 + 10 + 1 + 1 = 22

(ii) IX = 10 - 1 = 9

(iii) XIV = 10 + 5 - 1 = 14

(iv) XXXIX = 10 + 10 + 10 + 10 - 1 = 39

2. Write each of the following in a Roman numeral:

(i) 9

(ii) 14

(iii) 26

(iv) 31

(v) 37

Solution:

(i) 9 = IX

(ii) 14 = 10 + 4 = XIV

(iii) 26 = 10 + 10 + 5 + 1 = XXVI

(iv) 31 = 10 + 10 + 10 + 1 = XXXI

(v) 37 = 10 + 10 + 10 + 5 + 1 + 1 = XXXVII

3. The Roman numeral for 479 is

(i) CD

(ii) CCCXLVI

(iii) CDLXXIX

(iv) CDIXX

Solution:

479 = 400 + 70 + 9 = CDLXXIX

So, the option (iii) is correct, which is the required answer.

Understanding of Roman Numerals:

Matchsticks.

Each numeral is made of 2 matchsticks.

Each numeral is made of 3 matchsticks.

Each numeral is made of 4 matchsticks.

Activity:

Roman numeral are used in many places will analogue clocks and watches. Find out some other places where these are used.

## Questions and Answers on Roman Numerals:

1. What is the Addition Rule of Roman Numerals?

If a symbol of smaller value is written to the right of a symbol of greater value, the value is added.

For Example:

VI = 5 + 1 = 6,

XII = 10 + 1 + 1 = 12,

LXV = 50 + 10 + 5 = 65, etc.

Note: X can be repeated at the most 3 times.

2. What is the Subtraction Rule of Roman Numerals?

If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of greater symbol.

For Example:

IV = 5 - 1 = 4

IX = 10 - 1 = 9 etc.

Note: I can be subtracted from V and X only.

3. A group of digits denoting a number is called a __________.

4. What is the CDLX equals to

## Worksheet on Roman Numerals:

I. Write the corresponding Roman numerals.

 (i) 67(ii) 58(iii) 13(iv) 16(v) 29(vi) 36(vii) 5(viii) 26(ix) 81(x) 77(xi) 59(xii) 95 (xiii) 28(xiv) 22(xv) 38(xvi) 67(xvii) 447(xviii) 90(xix) 47(xx) 49(xxi) 24(xxii) 25(xxiii) 324(xxiv) 720

I.

 (i) 67 = LXVII(ii) 58 = LVIII(iii) 13 = XIII(iv) 16 = XVI(v) 29 = XXIX(vi) 36 = XXXVI(vii) 5 = V(viii) 26 = XXVI(ix) 81 = LXXXI(x) 77 = LXXVII(xi) 59 = LIX(xii) 95 = XCV (xiii) 28 = XXVIII(xiv) 22 = XXII(xv) 38 = XXXVIII(xvi) 67 = LXVII(xvii) 447 = CDXLVII(xviii) 90 = XC(xix) 47 = XLVII(xx) 49 = XLIX(xxi) 24 = XXIV(xxii) 25 = XXV(xxiii) 324 = CCCXXIV(xxiv) 720 = DCCXX

II. Write the corresponding Hindu-Arabic (Indian) numerals.

 (i) XCIX(ii) LVI(iii) XXVI(iv) XCVI(v) LXXXIII(vi) XXX(vii) XCI(viii) XXV(ix) LXIX(x) VI(xi) XVIII(xii) XXXII (xiii) XXXIX(xiv) LX(xv) XXIII(xvi) XXXV(xvii) XXXIV(xviii) XXVII(xix) XXVIII(xx) XXIV(xxi) XXI(xxii) LII(xxiii) XXXVI(xxiv) DLII

II.

 (i) XCIX = 99(ii) LVI = 56(iii) XXVI = 26(iv) XCVI = 96(v) LXXXIII = 83(vi) XXX = 30(vii) XCI = 91(viii) XXV = 25(ix) LXIX = 69(x) VI = 6(xi) XVIII = 18(xii) XXXII = 32 (xiii) XXXIX = 39(xiv) LX = 60(xv) XXIII = 23(xvi) XXXV = 35(xvii) XXXIV = 34(xviii) XXVII= 27(xix) XXVIII = 28(xx) XXIV = 24(xxi) XXI = 21(xxii) LII = 52(xxiii) XXXVI = 36(xxiv) DLII = 552

III. Write whether the following are true or false.

(i) XVI = 14

(ii) IV = 6

(iii) IX = 9

(iv) XL = 60

(v) XC = 90

III. (i) False

(ii) False

(iii) True

(iv) False

(v) True

IV. Fill in the correct sign '<', '>' or '='.

(i) XXIX _____ XXXI

(ii) XLV _____ LXV

(iii) XCII _____ XC

(iv) LXX _____ XL

(v) XCI _____ LXXI

(vi) IV _____ VI

(vii) XIX _____ XXI

(viii) XIX _____ XI

(ix) III _____ XIV

(x) 10 _____ XIX

(xi) XXIX _____ 33

(xii) XV _____ 15

(xiii) 16 _____ XVII

(xiv) XXXI _____ 28

(xv) 10 + 4 _____ XIV

(xvi) XXV _____ XXI

(xvii) XV _____ XX

IV. (i) XXIX < XXXI

(ii) XLV < LXV

(iii) XCII > XC

(iv) LXX > XL

(v) XCI > LXXI

(vi) IV > VI

(vii) XIX < XXI

(viii) XIX > XI

(ix) III < XIV

(x) 10 < XIX

(xi) XXIX < 33

(xii) XV = 15

(xiii) 16 < XVII

(xiv) XXXI > 28

(xv) 10 + 4 = XIV

(xvi) XXV > XXI

(xvii) XV < XX

V. Which of the following are meaningless?

(i) VX

(ii) IXIV

(iii) XIX

(iv) XVI

(v) VVV

(vi) XV

(vii) LL

(viii) LC

(ix) XVIII

(x) VL

V. (i) VX

(ii) IXIV

(iv) XVI

(v) VVV

(vii) LL

(viii) LC

(x) VL

VI: Solve and write the answers in Roman Numerals:

(i) 6 + 18 = _____

(ii) 36 - 6 = _____

(iii) XXI + XIII = _____

(iv) XXI - X = _____

(v) XXX - VII = _____

(vi) X + XI = _____

(vii) 50 - 25 = _____

(viii) 14 + 9 = _____

VI: (i) XXIV

(ii) XXX

(iii) VIII

(iv) XI

(v) XXIII

(vi) XXI

(vii) XXV

(viii) XXIII

VII. The Roman numeral for 986 is

(i) CMLXXIX

(ii) CMLXXXVI

(iii) MCXLIX

(iv) CMXLIX

VIII. State True or False

(i) 346 in Roman numerals equals to LXI

(ii) CMLXXXVIII equals to 988

VIII. (i) False

(ii) True

## You might like these

• ### Prime Triplet Numbers | Examples on Prime Triplet | Question Answer

A group of three consecutive prime numbers that differ by 2 is called a prime triplet. For example: (3,5,7) is the only prime triplet.

• ### Find the Missing Digits | Missing Digits in Addition and Subtraction

How to find the missing digits in the blank spaces? Add the ONES: 5 + 9 = 14 Regroup as 1 Ten and 4 Ones Add the TENS: 2 + 1 carry over = 3 Write 2 in the box to make 3 + 2 = 5 Add the HUNDREDS: 4

• ### Successor and Predecessor | Successor of a Whole Number | Predecessor

The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number. For example, 9,99,99,999 is predecessor of 10,00,00,000 or we can also

• ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

• ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.

• ### Place Value | Place, Place Value and Face Value | Grouping the Digits

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know that the position of a digit in a number determines its corresponding value

• ### Formation of Numbers with the Given Digits |Making Numbers with Digits

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and ‘-‘ signs. We find the sum of the numbers with ‘+’ sign and similarly the sum

• ### Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) VII (b) IX (c) XI (d) XIV (e) XIX (f) XXVII (g) XXIX (h) XII

• ### International Place-value Chart | International Place-value System

In International place-value system, there are three periods namely Ones, thousands and millions for the nine places from right to left. Ones period is made up of three place-values. Ones, tens, and hundreds. The next period thousands is made up of one, ten and hundred-thous

• ### Worksheet on Formation of Numbers | Questions on Formation of Numbers

In worksheet on formation of numbers, four grade students can practice the questions on formation of numbers without the repetition of the given digits. This sheet can be practiced by students

• ### Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn

• ### Worksheets on Comparison of Numbers | Find the Greatest Number

In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

• ### Dividing 3-Digit by 1-Digit Number | Long Division |Worksheet Answer

Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit number. I: Dividing 3-digit Number by 1-Digit Number without Remainder:

• ### 4th Grade Mental Math on Factors and Multiples |Worksheet with Answers

In 4th grade mental math on factors and multiples students can practice different questions on prime numbers, properties of prime numbers, factors, properties of factors, even numbers, odd numbers, prime numbers, composite numbers, tests for divisibility, prime factorization

Related Concept

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

Jul 22, 24 03:27 PM

Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

2. ### Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

Jul 22, 24 02:41 PM

Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

3. ### Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

Jul 21, 24 02:14 PM

Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

4. ### Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

Jul 20, 24 03:45 PM

When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…