NCERT Class 6 Mathematics Textbook for blind and visually impaired students made Screen Readable by Professor T K Bansal.

So far, we have been using the Hindu-Arabic numeral system. This is not the only system available. One of the early systems of writing numerals is the system of Roman numerals. This system is still used in many places.

For example, we can see the use of Roman numerals in wall clocks; it is also used for classes in the school time table etc.

Find three other examples, where Roman numerals are used.

The Roman numerals :

I, II, III, IV, V, VI, VII, VIII, IX, X denote 1,2,3,4,5,6,7,8,9 and 10 respectively. This is followed by XI for 11, XII for 12,... till XX for 20. Some more Roman numerals are :

I = 1,
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

The rules for the system are as follows:

(a) If a symbol is repeated, its value is added as many times as it occurs:
i.e. II is equal 2, XX is 20 and XXX is 30.

(b) A symbol is not repeated more than three times. But the symbols V, L and D are never repeated.

(c) If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.
VI = 5 + 1 = 6, XII = 10 + 2 = 12 and LXV = 50 + 10 + 5 = 65

(d) 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 the greater symbol.
IV = 5 − 1 = 4, IX = 10 − 1 = 9
XL= 50 − 10 = 40, XC = 100 − 10 = 90

(e) The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted.

The symbol I can be subtracted from V and X only.
The symbol X can be subtracted from L, M and C only.

Following these rules we get,
1 = I
10 = X
100 = C
2 = II
20 = XX
3 = III
30 = XXX
4 = IV
40 = XL
5 = V
50 = L
6 = VI
60 = LX
7 = VII
70 = LXX
8 = VIII
80 = LXXX
9 = IX
90 = XC

(a) Write in Roman numerals the missing numbers in the table.
(b) XXXX, VX, IC, XVV are not written. Can you tell why?

Try These 1.19

Write in Roman numerals.
1. 73
2. 92

Example 7

Write in Roman Numerals
(a) 69
(b) 98.

Solution:

(a) 69 = 60 + 9
= (50 + 10) + 9
= LX + IX
= LX IX

(b) 98
= 90 + 8
= (100 − 10) + 8
= XC + VIII
= XCVIII