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ROMAN NUMERALS
Let’s recall ...
Roman numeral system was developed by the ancient Romans. It is based on seven letters of
the alphabet. All the numbers are written using either one letter or a combination of letters.
However, there is no letter representing zero.
The seven letters used in the Roman numeral system and their corresponding values in HinduArabic numeral system are given in the following table.
Roman Numeral
I
V
X
L
C
D
M
Hindu-Arabic Numeral
1
5
10
50
100
500
1,000
Let’s learn further ...
In modern Roman numeral system, for large numbers a bar is placed above the base numeral
indicating multiplication by 1,000, although the ancient Romans themselves often just used
M for it.
V
Five thousand
X
Ten thousand
L
Fifty thousand
C
One hundred thousand
D
Five hundred thousand
M
One million
Rules for Subtracting Values in Roman Numerals
1. Subtract only the values of letters I, X and C. Values of V, L and D cannot be subtracted.
Consider the numeral 45.
45 = XLV [(50 – 10) + 5] 45 ≠ VL (50 – 5)
2. Subtract the value of only a single smaller numeral from a single bigger numeral. In other
words, you can subtract only once from a numeral. Consider the numeral 8.
8 = VIII (5 + 3)
8 ≠ IIX (10 – 1 – 1)
3. Do not subtract a numeral from another numeral which is more than 10 times greater, i.e.,
I can be subtracted from V and X but not from L, C, D and M. Similarly, X can be subtracted
from L and C but not from D, M and so on ...
Conversion of Roman Numeral to Hindu-Arabic Numeral
1. If a smaller number is to the left of a larger number, subtract the value of the smaller
number from the larger number.
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Consider the number IX. Since I < X, 10 – 1 = 9. Therefore, IX = 9. Also, in XL, X < L.
Therefore, XL = 50 – 10 = 40.
2. If a smaller number is to the right of a larger number, add the value of the smaller number
to the larger number.
Consider the number XI. Since X > l, 10 + 1 = 11. Therefore, XI = 11.
3. If the number has more than two letters, add the value of each letter to find the number.
Consider the number LXVIII. LXVIII = 50 + 10 + 5 + 1 + 1 + 1 = 68.
Also, CDI = (CD) + 1 = (500 – 100) + 1 = 400 + 1 = 401.
Remember
Conversion of Hindu-Arabic Numeral to Roman
Numeral
Numbers 1, 2, 3 are written in Roman numerals as I, II and
III, respectively. Now 4 cannot be written as IIII since the To subtract, the smaller
symbol is placed before
symbol I can be repeated only three times in a row.
Let’s learn how to write 4 in Roman numerals.
4 < 5 and 4 = 5 – 1 = V – I
Therefore, 4 = IV.
Now let’s learn how to write 6 in Roman
numerals.
the bigger symbol.
To add, the smaller
symbol is placed
after the bigger
symbol.
6 > 5 and 6 = 5 + 1 = V + I
Therefore, 6 = VI.
Similarly, 7 = 5 + 2 = VII and 8 = 5 + 3 = VIII. But 9 cannot be written as VIIII as I cannot be
repeated more than three times.
Let’s learn how to write 9 in Roman numerals.
9 < 10 and 9 = 10 – 1 = X – I
Therefore, 9 = IX.
Also, 11 > 10 and 11 = 10 + 1 = X + I
I, X, C and M can be repeated
only three times in a row.
V, L and D cannot be repeated
at all.
Therefore, 11 = XI.
Similarly, 40 = 50 – 10 = L – X = XL
And, 90 = 100 – 10 = C – X = XC
To convert a large Hindu-Arabic numeral to a Roman numeral, convert each digit separately
and then combine the letters.
Example 1: Convert 752 into Roman numeral.
Solution:
752= 700 + 50 + 2
= DCC + L + II = DCCLII
Try this!
Write 999 in Roman
numerals.
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Roman Numerals up to Hundred
1
2
3
4
5
6
7
8
9
10
I
II
III
IV
V
VI
VII
VIII
IX
X
11
12
13
14
15
16
17
18
19
20
XI
XII
XIII
XIV
XV
XVI
XVII
XVIII
XIX
XX
21
22
23
24
25
26
27
28
29
30
XXI
XXII
XXIII
XXIV
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
31
32
33
34
35
36
37
38
39
40
XXXI
XXXII
XXXIII
XXXIV
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
41
42
43
44
45
46
47
48
49
50
XLI
XLII
XLIII
XLIV
XLV
XLVI
XLVII
XLVIII
XLIX
L
51
52
53
54
55
56
57
58
59
60
LI
LII
LIII
LIV
LV
LVI
LVII
LVIII
LIX
LX
61
62
63
64
65
66
67
68
69
70
LXI
LXII
LXIII
LXIV
LXV
LXVI
LXVII
LXVIII
LXIX
LXX
71
72
73
74
75
76
77
78
79
80
LXXI
LXXII
LXXIII
LXXIV
LXXV
LXXVI
LXXVII
LXXVIII
LXXIX
LXXX
81
82
83
84
85
86
87
88
89
90
LXXXI
LXXXII
LXXXIII
LXXXIV
LXXXV
91
92
93
94
95
96
97
98
99
100
XCI
XCII
XCIII
XCIV
XCV
XCVI
XCVII
XCVIII
XCIX
C
LXXXVI LXXXVII LXXXVIII LXXXIX
Addition and Subtraction of Roman Numerals
To add or subtract Roman numerals, follow these steps.
• Change the number into Hindu–Arabic numbers.
• Add or subtract accordingly.
• Convert the answer into Roman numeral.
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Example 2:
Solution:
XLV + LXIII
XLV = 45
LXIII = 63
45 + 63 = 108 = CVIII
Therefore, XLV + LXIII = CVIII
Example 3:
Solution:
CCXCVI – CLXXIV
CCXCVI = 296
CLXXIV = 174
296 – 174 = 122 = CXXII
Therefore, CCXCVI – CLXXIV = CXXII
Try these!
Find the sum.
(a)MIX + I=
(b)MIX – I=
Maths Fun
How can half
of XII be 7?
XC
Modern Usage
Roman numerals were commonly used until 14th century. Since they were not enough to write
large numbers, they were replaced by Hindu-Arabic numbers. However, we still see them being
used in certain places in modern times. Some of them are given below.
• Names of Monarchs and Popes like, Elizabeth II and Benedict XVI
• Hour marks on clock faces and timepieces
• Recurring grand event such as Olympic games
• Sometimes page numbering and chapter numbering
XII
XI
I
II
X
IX
III
VIII
VII
IV
V
VI
LET’S EVALUATE
1. Convert the following Hindu-Arabic numbers to Roman numerals.
(a) 15 = _______
(b) 49 = _______
(c) 103= _______
(d) 305= _______
(e) 228= _______
(f ) 450= _______
(g) 637= _______
(h) 989= _______
(i) 354= _______
(j) 509= _______
(k) 83 = _______
(l) 179= _______
2. Convert the following Roman numerals to Hindu-Arabic numbers.
(a) XIV
= _______
(b) LXII = _______
(c) XCVIII
= _______
(d) CCCXXXI= _______
(e) CDV = _______
(f ) CMLXXVI= _______
(g) DCCI
= _______
(h) CMXV= _______
(i) CD
= _______
(j) LIII = _______
(k) XLIX = _______
(l) DCII
= _______
3. Find the value of the following Roman numerals.
(a) LXXXIV + XXVI
(b) XCIII + LXXI
(c) CCXCI – CVI
(d) DXLVI – CDXX
(e) LX + XII
(f ) XXIX + XIV
(g) XL – XIX
(h) XCIX – XIII
(i) XXXIX – XIX
4. What comes before or after the given Roman numerals?
(a) ________, XXXIV
(b) ________, C
(c) XXXIX, ________
(d) CCCXCIX, _________
(e) XXI, ________
(f ) XLIX, ________
(g) ________, LXX
(h) ________, XC
(i) ________, DXLVI
5. Put the correct sign <, > or =.
(a)46
XXV
(b) CCLV
245
(c) XC
CX
(d)CL
150
(e) XLII + 12
LXXIV – XXXVIII
(f ) C
50
6. Change the Hindu-Arabic numerals to Roman numerals and solve the following. Write the
answer in Roman numerals.
(a) 400 + 13
(b) 50 – 27
(c) 37 + 12
(d) 29 – 9
(e) 733 – 20
(f ) 100 + 65
(g) 80 – 30
(h) 250 + 45
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SCRATCH YOUR BRAIN (HOTS)
1. There are seven letters used as Roman numerals I, V, X, L, C, D and M.
(a) Which is the biggest correctly formed Roman numeral using each numeral once?
(b) Which is the smallest correctly formed Roman numeral using each numeral once?
2.Form two Roman numerals that are also words in English. For example, MIX is a Roman
numeral and an English word.
MATHS LAB ACTIVITIES
1. Cut and paint a clock face from a cardboard sheet. Mark the hours in Roman numerals.
2. Using glue and matchsticks or toothpicks, design a birthday greeting with your birth
date marked in Roman numerals.
3. Read the given riddle carefully.
RAM SAXENA GOES TO THE CHURCH ON THE SIXTH OF MAY.
In which year was he born?
(Hint: Find all the Roman numerals and arrange correctly.)
Answer: MCMXCIX, i.e., 1999
Form groups, make more such riddles and have a class competition.
HISTORY OF ROMAN NUMERALS
Ancient Romans used only capital (upper case) letters to write numerals. However, during medieval
age small (lower case) letters like i, ii, iii, etc. were developed and used. Further during the medieval
age, practice of substituting ‘j’ for the last numeral to end numbers was adopted. For example, iiij
became 4 and viij became 8. This was done to prevent tempering after the numbers had been written.
Also, earlier Romans made notch marks on wooden sticks to show
numbers. Thus ‘I’ came from a vertical notch mark ‘I’ across the stick.
Every fifth notch was double-cut like ‘V’ and every tenth notch was crosscut like ‘X’. The notching pattern was IIIIVIIIIXIIIIVIIIIXII ... .
This produced a positional system, ‘7’ on a counting stick meant 7 notches
IIIIVII which could be abbreviated as VII as the existence of V implies
4 prior notches. Likewise, ‘16’ was the 6th notch after ten which could
be abbreviated as X. So, the number 16 became XVI. Interestingly, the
Romans drew an extra stroke for every tenth V or X. The hundredth V
or X were marked with a box or circle. And finally, 1000 was marked as
circled or boxed X.
I
I
I
I
V
I
I
I
I
X
Another interesting fact you should know is that ancient Romans were smart enough to have a
calculating machine like a modern calculator that could fit in a shirt’s pocket. It was the Roman
abacus which besides doing basic calculations could also do fractions. This Roman abacus was
similar to the Chinese abacus ‘Suanpan’ or the modern Japanese abacus ‘Soroban’.
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