ROMAN NUMERALS
Roman numerals are a numeral system which was devised by the ancient Romans long ago. In this system, numbers are represented by combination of letters from the Latin alphabet.
Modern Roman numerals use seven symbols, each with a fixed integer value. The following table shows the seven symbols and their values.
|
Symbol |
I |
V |
X |
L |
C |
D |
M |
|
Value |
1 |
5 |
10 |
50 |
100 |
500 |
1000 |
RULES FOR WRITING ROMAN NUMERALS
The seven symbols of Roman numerals are used in different combinations to represent different numbers. There are some rules which govern the combination of symbols.
Rule 1: Rule of Multiplication
When a symbol is repeated in succession, we multiply the value of the symbol by the number of times it is repeated.
For example, III = 3 x 1 = 3
XX = 2 x 10 = 20
CC = 2 x
100 = 200
NOTE:
1. A symbol
cannot be repeated more than three times in succession.
e.g. We cannot write 40 as XXXX.
2. Only the
symbols I, X, C and M are repeated.
3. The symbols
V, L and D cannot be repeated.
Rule 2: Rule of Addition
When a
symbol of smaller value is written to the right of a symbol of greater value,
the smaller value is added to the greater value.
For example,
VI = 5 + 1 = 6
XI = 10 + 1 = 11
LXI = 50 +10 + 1 = 61
Rule 3: Rule of Subtraction
When a
symbol of smaller value is written to the left of a symbol of greater value,
the smaller value is subtracted from the greater value.
For example,
IV = 5 – 1 = 4
IX = 10 – 1 = 9
XC = 100 – 10 = 90
1. Symbols V,
L and D are never subtracted.
2. The symbol
I is subtracted from V and X only.
IV = 5 – 1 = 4 (Correct)
IL = 50 – 1 = 49 (Incorrect)
IC = 100 – 1 = 99 (Incorrect)
3. The symbol
X is subtracted from L and C only.
XL = 50 – 10 = 40 (Correct)
XD = 500 – 10 = 490 (Incorrect)
XM = 1000 – 10 = 990 (Incorrect)
4. The symbol
C is subtracted from D and M.
CD = 500 – 100 = 400 (Correct)
CM = 1000 – 100 = 900 (Correct)
Rule 4: Rule of Precedence
When a
symbol of smaller value is placed between two symbols of greater value, the
smaller value always is subtracted from the greater value which is to its
right.
For example,
XIV = 10 + (5 – 1) = 14 (Correct)
XIV = 10 + 1 + 5 = 16
(Incorrect)
CXL = 100 + (50 – 10) = 140 (Correct)
CXL = 100 + 10 + 50 = 160 (Incorrect)
SOME BASIC ROMAN NUMERALS
Roman Numerals for 1 to 10
|
Hindu-Arabic Numerals |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Roman Numerals |
I |
II |
III |
IV |
V |
VI |
VII |
VIII |
IX |
X |
Roman numerals for some
other basic numbers
|
Hindu-Arabic Numerals |
Roman Numerals |
|
Hindu-Arabic Numerals |
Roman Numerals |
|
Hindu-Arabic Numerals |
Roman Numerals |
|
10 |
X |
|
100 |
C |
|
1000 |
M |
|
20 |
XX |
|
200 |
CC |
|
2000 |
MM |
|
30 |
XXX |
|
300 |
CCC |
|
3000 |
MMM |
|
40 |
XL |
|
400 |
CD |
|
|
|
|
50 |
L |
|
500 |
D |
|
|
|
|
60 |
LX |
|
600 |
DC |
|
|
|
|
70 |
LXX |
|
700 |
DCC |
|
|
|
|
80 |
LXXX |
|
800 |
DCCC |
|
|
|
|
90 |
XC |
|
900 |
CM |
|
|
|
ROMAN
NUMERALS FOR LARGER NUMBERS
The symbols of Roman numerals cannot be repeated more than three times. Thus, the biggest number that we can form in Roman numerals is MMMCMXCIX, or 3,999.
But there are ways we can represent numbers even higher than this. One method is to draw a horizontal line or bar across a Roman numeral to multiply it by 1,000.
For example, 5000 is
written as 
;
9000
is written as 
and so
on.
Another way of writing
even a larger number is to place a partial frame (a frame which is open at the bottom) around a Roman numeral to indicate that the framed number
is to be multiplied by 1,00,000.
For example,
ILLUSTRATIVE EXAMPLES
Example 1:
Write the following in Roman numerals:
(a) 78 (b) 256
(c) 539
(d) 944 (e) 2020
Solution: (a) 78 = 70
+ 8 =
LXX + VIII = LXXVIII
(b) 256 = 200 + 50 + 6
= CC + L + VI =
CCLVI
(c) 539 = 500 + 30 + 9
= D + XXX + IX = DXXXIX
(d) 944 = 900 + 40 + 4
= CM + XL + IV = CMXLIV
(e) 2020 = 2000 + 20
= MM + XX = MMXX
Example 2:
Write the Hindu-Arabic numeral for each of the following:
(a) CLIX (b) DCL (c) CCXXII (d) MLI (e) DXC
Solution: (a) CLIX = C + L
+ IX =
100 + 50 + (10 – 1) = 159
(b) DCL = D + C + L = 500 + 100 + 50 = 650
(c) CCXXII = CC + XX + II =
200 + 20 + 2 = 222
(d) MLI = M + L + I = 1000 +
50 + 1 = 1051
(e) DXC = D + XC = 500 +
(100 – 10) = 590
 |
EXERCISE
1. Write the following in Roman numerals:
(a) 258
(b) 410 (c) 385 (d) 135 (e) 555
(f) 989 (g) 1247 (h) 2021 (i) 6874 (j) 8001
(k) 25613 (l) 23918 (m) 99999 (n) 239184 (o) 123456
2. Write the Hindu-Arabic numeral for each of the following:
(a) XLV (b)
LVII (c) XCVIII (d) LXXXVI (e) CIII
(f) MV (g) DL (h) MMDCC (i) MIX (j) MD
3. Choose the right answer:
(i) The greatest numeral in the given set
is:
(a) XXXV (b)
XXIX (c)
XLIV (d) LX
(ii) The Roman numeral for 95 is:
(a) XCV (b) VC (c) IXV (d) CV
(iii) The Roman numeral for 999:
(a) IXIXIX (b) CMXCIX (c) IM
(d) XCIX
(iv) Twelve dozens is equal to:
(a) XIID (b)
CLXIV (c) CDIV (d)
CXLIV
(v) The Roman numeral for 905 is:
(a) DCV (b)
CDV (c) CMV
(d) IXV
(vi) CXL represents:
(a) 100 + 10 + 50 (b) 100 + 50 + 10
(c) 100 + (50 – 10) (d) 100 – (50 + 10)
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