The Roman Number System
The Roman numerals are a number system which originated in ancient
Rome and used widely in Europe. Only in 14th century, they were
getting replaced gradually by Hindu-Arabic numerals.
The seven symbols used in Roman numerals are shown
below in the table with their corresponding Hindu-Arabic numerals.
|
I |
V |
X |
L |
C |
D |
M |
|
1 |
5 |
10 |
50 |
100 |
500 |
1000 |
Rules to Form Roman Numerals
Rule 1: If a symbol is written
twice or thrice, the value of the numeral is obtained by adding the value of the
symbol as many times as it is written.
For example: III = 1 + 1 + 1 = 3; XX = 10 + 10 = 20; CCC
= 100 + 100 + 100 = 300
Rule 2: The symbols I, X, C
and M can be written to a maximum of three times.
Rule 3: The symbols V, L and D
cannot be repeated.
Rule 4: If a symbol of smaller
value is written to the right of another symbol of greater value, we add their values.
For example: XII = 10 + 1 + 1 = 12; DCC = 500 + 100 +
100 = 700
Rule 5: If a symbol of smaller
value is written to the left of another symbol of greater value, we subtract their
values.
For example: IX = 10 − 1 = 9; CD = 500 − 100 = 400
Note: The symbols V, L and D
cannot be written to the left of symbols of greater value. The symbol I can be
written to the left of V and X only. The symbol X can be written to the left of
L and C only. The symbol C can be written to the left of D and M only.
Solved Examples
Example 1: Write the Roman Numerals for the following
Hindu-Arabic numbers.
a. 29 = 10 + 10 + 9
= 10 + 10 + (10 – 1)
= XXIX
b. 459 = 400 + 50 + 9
= (500 – 100) +
50 + (10 – 1)
= CDLIX
c. 1253 = 1000 + 100 + 100 + 50 + 3
= MCCLIII
d. 1916 = 1000 + 900 + 10 + 6
= 1000 + (1000
– 100) + 10 + (5 + 1)
= MCMXVI
Example 2: Write the
Hindu-Arabic numerals for the following Roman numerals.
a. XXI = 10 + 10 + 1 = 21
b. XCVI = (100 − 10) + 5 + 1 = 96
c. DCCV = 500 + 100 + 100 + 5 = 705
d. MCCC = 1000 + 100 + 100 + 100 = 1300
Example 3: Add the following Roman Numerals without
converting them to Hindu Numerals.
a. CCCXXII + CCXLIII
There are 5 Cs, 2 Xs, 1 XL, and 5 Is. The XL amounts to 4 Xs. So,
in all we have, 5 Cs, 6 Xs and 5 Is. The 5 Cs make a D, 6 Xs equals LX, and 5 Is
make V. So, CCCXXII + CCXLIII = DLXV
b. DCDXXI + CCCXXXII
First covert CD to 4 Cs. Thus, the given sum equals the sum of 1 D,
7 Cs, 5 Xs and 3 Is. The 7 Cs equals DCC. Now, we have 2 Ds, 2 Cs, 5 Xs and 3 Is.
The 2 Ds make one M and 5 X = L.
So, DCDXXI + CCCXXXII = MCCLIII
Exercise
1. Write the Roman Numerals for the following Hindu-Arabic
numbers.
a. 499 b. 1659 c. 925 d. 2124
2. Write the Hindu-Arabic numerals for the
following Roman numerals.
a. CCCXIII b.
DCXXIV c. CDLXXXV d. MDCLXIX
3. The capacity of an auditorium is 426. Express this number as a
Roman Numeral.
4. In a school of 4000 children, 2875 students play cricket. The
remaining students play football. Write down the number of students who play
cricket and football in Roman Numerals.
5. Add the following Roman Numerals without converting them to Hindu
Numerals.
a. DCCLXXI + MCXXXIII b. MMCCXIX + DCXXVI