# Roman Numerals

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 Roman numerals in clocks
• they are used to number pages that come before the main pages of a book
• they are used to identify kings and queens (for example, Henry VIII of England)
• they are used to identify sporting events (like, The New York Giants won Super Bowl XLII).

They use the following seven letters of the alphabet to write all numbers.

There is no zero (0) in the Roman system. The Roman system does not use place value concept. The Roman numerals I, II, III, IV, V, VI, VII, VIII, IX, X respectively denote 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This is followed by XI for 11, XII for 12, . . . , till XX for 20. The traditional Roman numeral system was only used for numbers up to 3,999 which is represented as MMMCMXCIX.

##### The rules for the system

(a) If a symbol is repeated, its value is added as many times as it occurs.

For example,

• II is equal 2
• XX is 20
• XXX is 30.

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

Hence, IIII, XXXXX are not valid.

(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.

For example,

• VI = 5 + 1 = 6
• XII = 10 + 2 = 12
• XXVII = 10 + 10 + 5 + 1 + 1 = 27
• LXV = 50 + 10 + 5 = 65
• MDC = 1000 + 500 + 100 = 1600

(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.

For example,

• 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. In other words, V, L and D are never subtracted.

(f) The symbol I can be subtracted from V and X only.

(g) The symbol X can be subtracted from L, M and C only.

Example. Write 69 in Roman Numerals.

Solution. We can write

69 = 60 + 9

= (50 + 10) + 9

= LX + IX

= LXIX

Example. Write 98 in Roman Numerals98.

Solution. We can write

98 = 90 + 8

= (100 – 10) + 8

= XC + VIII

= XCVIII

Example. Can we write 40 as XXXX?

Solution. No.

As we cannot repeat the symbol X for more than three times.

Example. How to write 800 in Roman numeral?

Solution. We can write, 800 = 500 + 100 + 100 + 100

We know that, 500 = D and 100 = C.

Therefore, 800 = DCCC.

Example. Write 3249 in the Roman number system.

Solution. We can write

3249

= 3000 + 200 + 40 + 9

= MMM + CC + XL + IX

= MMMCCXLIX

Example. Write MDCLXVII in the Hindu-Arabic system.

Solution. We can write

MDCLXVII

= M + DC + LX + VII

= 1000 + 600 + 60 + 7

= 1667

Below is the list of all Roman numerals up to 1000.

Roman Numerals 1 to 100

Roman Numerals 101 to 200

Roman Numerals 201 to 300

Roman Numerals 301 to 400

Roman Numerals 401 to 500

Roman Numerals 501 to 600

Roman Numerals 601 to 700

Roman Numerals 701 to 800

Roman Numerals 801 to 900

Roman Numerals 901 to 1000