Page 18 - Maths Class 06

Roman Numbers
In Hindu-Arabic numeration system we use ten digits : 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write numerals for
any number. People in ancient India developed this set of ten digits and the method of writing a numeral
for any number using these ten digits. Later on, these were spread by Arabs to the other Countries. Hence,
numerals formed by these ten digits are popularly known as Hindu-Arabic numerals.
Unlike Hindu-Arabic numerals, in ancient days Roman had a different system of numeration. They used
only seven symbols to write numerals for numbers. These symbols are I, V, X, L, C, D and M. Each letter
has a different value, respective values of these seven symbols are as under:

I V X L C D M

1 5 10 50 100 500 1000

NOTE
In Roman numeration system, there is no symbol for zero. Also, this system is not a place value system.

We still use Roman numerals in our day-to-day contexts. Sometimes the units of a book and classrooms in
a school are marked in Roman numerals. Roman numerals can also be seen on clocks and watches.

How Roman Numerals are Formed?
Roman numerals are formed by writing the above seven symbols in different combinations following
certain rules. We state these ruled below. However, we shall restrict the study of Roman numerals upto
100 only.
Rule 1. When a symbol is repeated twice or thrice, the value of the numeral is obtained by adding the
value of the symbol as many times as it is repeated.

For example, III = + + =1 1 1 3
XXX = 10 + 10 + 10 = 30

CC = 100 + 100 = 200
The symbols V, L D are never repeated.
No Roman symbol is repeated more than three times.

Caution : It is wrong to write 4 as IIII and 15 as VVV.

NOTE

Only powers of 10 can be repeated i.e., I, X, C, M can only be repeated.
Numeral I can only be subtracted from V and X.
Numeral X can only be subtracted from L, M and C.
The symbol V, L and D are never written to the left of a symbol of greater value.

Rule 2. When a symbol is written on the right of one of greater value, we add its value to the value of the
symbol on its left.

For example, VI = + =5 1 6
XII = 10 + + =1 1 12
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