1. Roman numerals
-Rules for writing

2. Rules for Formation of Roman-numerals
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. 

3. (b) The value of I, X and C are added as:
Rule 1: The roman digits I, X and C are repeated up to 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 = X = 10
II = = 2 XX = = 20
III = = XXX = = 30

4. (c) No digit is repeated in succession more than thrice, i. e
(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.

5. VI = 5 + 1 = 6 VII = 5 + 1 + 1 = 7 VIII = 5 + 1 + 1 + 1 = 8
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 = = 6
VII = = 7
VIII = = 8
XI = = 11
XII = = 12
XV = = 15
XVI = = 16
LX = = 60
LXV = = 65

6. 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 = = 4
IX = = 9
XL = = 40
XIV = 10 + (5 - 1) = 14 
XIX = 10 + (10 - 1) = 19
XXIX = (10 - 1) = 29
XLV = ( ) + 5 = 45
CLIX = (10 - 1) = 159

7. 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 = = = XII
20 = = XX
22 = = XXII
26 = = XXVI
39 = (10 - 1) = XXXIX
37 = = XXXVII

8. XV = 15 but XV = 15000, CLV = 155 but CLV = 155000
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 =