Roman Numerals

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Unit: Number System

Chapter: Roman Numerals

Reference: – Introduction to Roman Numerals, Seven Basic Symbols (I, V, X, L, C, D, M), Rules of Combination (Addition & Subtraction), Repetition Rules, Subtractive Notation, Large Numbers (Vinculum/Overline), Comparison with Hindu-Arabic System, Modern Uses

After studying this chapter, you should be able to understand:

• Introduction to Roman Numerals & Their Origin
• The Seven Basic Symbols and Their Values
• Rules for Combining Symbols (Addition & Subtraction)
• Repetition and Subtractive Notation Rules
• Writing Large Numbers (Vinculum/Overline)
• Converting Between Roman and Hindu-Arabic Numerals
• Modern Applications of Roman Numerals

Roman Numerals

 

The Hindu-Arabic numerals consist of a set of ten symbols i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 that originated in India and was later introduced to Europe through the writings of Middle Eastern mathematicians.

Till now we have learnt about the Hindu-Arabic system, but this is not the only system of numeration. We have seen different type of numerals used in clocks or for representing classes. This is referred as the Roman Numeral system.

 

• Roman Numeral system is one of the early systems of writing numerals.
• In The Roman Numeral system there are 7 symbols i.e. I, V, X, L, C, D and M unlike Hindu-Arabic, which has 10 symbols.
• The Roman Numerals do not follow a place value system and each symbol has a certain value given to it.

       

• There is no symbol for ‘0’ in this system.

 

 

The Roman Numerals for the numbers 1-10 are shown below-

 

This is followed by XI for 11, XII for 12,… till XX for 20.

 

Rules for Roman Numeral System

 

• Any symbol in Roman numerals is not repeated more than three times.

For example, 40 in Roman Numberals is written as XL and not XXXX.

 

• The symbols V, L and D are never repeated.

For example, 150 in Roman Numerals is written as CL and not LLL.

 

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

For example, II is equal 2, XX is 20 and XXX is 30.

 

• 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

and LXV = 50 + 10 + 5 = 65    

 

• 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

 

• If a symbol of smaller value is written between the symbols of greater value, then its value is subtracted from the symbol of the greater value which is wriiten immediately after the symbol of the smaller value.

For example, the value of XIV is 10 + (5 – 1) i.e. 14.

 

• The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted.

For example, the number 45 in Roman Numerals is written as XLV i.e. 50-10+5 and not VL i.e. 50-5.

 

• The symbol I can be subtracted from V and X only.

For example, we write 49 in Roman Numerals as XLIX i.e. 50 – 10 + (10 – 1) and not L – I i.e. 50-1.

 

• The symbol X can be subtracted from L, M and C only.

For example, we write 450 in Roman Numberals as CDXC i.e. 500 – 50 + 50 - 10 and not as XD i.e. 500 – 10.

 

Examples-

Write in Roman Numerals:

• 32

= 30 + 2

= XXXII

• 53

= 50 + 3

= LIII

• 78

= 50 + 20 + 8

= LXXVIII