Rules for Formation of Roman-numerals

In rules for formation of Roman-numerals system there is no symbol or digit for zero. This system has no place value system. The digit or digits of lower value is/are placed after or before the digit of higher value. The value of digits of lower value is added to or subtracted from the value of digit of higher value. Using the certain rules for formation of Roman-numerals is given below.

Rule 1: The roman digits I, X and C are repeated upto three times in succession to form the numbers.

(a) We know the value of I = 1, value of X is 10 and value of C is 100.


(b) The value of I, X and C are added as:

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

(c) No digit is repeated in succession more than thrice, i.e., I, X and C cannot be repeated more than 3 times.


(d) The digits V, L and D are not repeated. The repetition of V, L and D is invalid in the formation of numbers.


Rule 2: (a) When a digit of lower value is written to the right or after a digit of higher value, the values of all the digits are added. As:

VI = 5 + 1 = 6

VII = 5 + 1 + 1 = 7

VIII = 5 + 1 + 1 + 1 = 8

XI = 10 + 1 = 11

XII = 10 + 1 + 1 = 12

XV = 10 + 5 = 15

XVI = 10 + 5 + 1 = 16

LX = 50 + 10 = 60

LXV = 50 + 10 + 5 = 65


(b) Value of similar digits are also added as indicated in rule 1

III = 1 + 1 + 1 = 3


XXX = 10 + 10 + 10 = 30

XX = 10 + 10 = 20

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

IV = 5 - 1 = 4

IX = 10 - 1 = 9

XL = 50 - 10 = 40

XIV = 10 + (5 - 1) = 14

XIX = 10 + (10 - 1) = 19

XXIX = 10 + 10 + (10 - 1) = 29

XLV = (50 - 10) + 5 = 45

CLIX = 100 + 50 + (10 - 1) = 159

However, V is never written to the left of X.


Rule 4: (a) If we have to write the numbers beyond 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. As:

12 = 10 + 2 = 1 0 + 1 + 1 = XII

20 = 10 + 10 = XX

22 = 10 + 10 +1 + 1= XXII

26 = 10 + 10 + 5 + 1 = XXVI

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

37 = 10 + 10 + 10 + 5 + 1 + 1 = XXXVII


(b) According to this pattern, numbers higher than number 40 are also formed:

43 = (50 - 10) + 1 +1 + 1= XLIII

56 = 50 + 5 + 1 = LVI1

59 = 100 + 50 + (10 - 1) = CLIX

1238 = 1000 + 100 + 100 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = MCCXXXVIII


Rule 5: If a horizontal line is drawn over the symbols or digits of Roman numerals, then the value of the numerals becomes 1000 times. As:

XV = 15 but XV = 15000,

CLV = 155 but CLV = 155000

For example:

1. Write the Roman numerals for the following numbers:

(i) 13 = XIII

(ii) 14 = XIV

(iii) 18 = XVIII

(iv) 26 = XXVI

(v) 39 = XXXIX

(vi) 42 = XXXXII

(vii) 61 = LXI

(viii) 545 = DXLV

(ix) 217 = CCXVII

2. Write the numbers for the following Roman numerals:

(i) VII = 7

(ii) XXXIV = 34

(iii) XXXVII = 37

(iv) XLIII = 43

(v) XLVIII = 48

(vi) LII = 52

(vii) CXL = 140

(viii) CXLV = 145

These are the five rules for formation of Roman-numerals system explained using examples.

Related Concept

Roman Numerals

Rules for Formation of Roman-numerals

Uses of Roman Numerals


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