Rules of Roman Numeration

We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500 and 1000 respectively. We already learned about the numerals I, V, X, L and C and now we will learn about the remaining two numerals.

There is another symbol ‘─’ which is called bar. If bar is place over a numeral, it is multiplied by 1000. Thus, V and XII stand for 5000 and 12000 respectively.

Rules of Roman Numeration:

1. First Rule: Numerals of the same value are added.

When the same symbol is repeated, the value of the symbol is added to get the value of the numeral. I, X and C can be repeated only up to three times. Symbols V, L and D are never repeated.

For example:

I I I stands for 1 + 1 + 1 = 3

XX = 10 + 10 = 20

X X X stands for 10 + 10 + 10 = 30

CC = 100 + 100 = 200

C C C stands for 100 + 100 + 100 = 300

M M M stands for 1000 + 1000 + 1000 = 3000

Note:

(i) Symbols V, L and D are not repeated.

(ii) A symbol cannot be repeated more than three times.

2. Second Rule: A symbol of smaller value put on the right of greater value symbol is added to it.

The values of the symbols are added or subtracted to find the values of the Roman numerals. When the smaller numeral is written to the right of a greater numeral, the value of the smaller numeral is added to the greater numeral.

For example:

VI stands for 5 + 1 = 6

CV = 100 + 5 = 105

CX = 100 + 10 = 110

CXX stands for 100 + 10 + 10 = 120

DC = 500 + 100 = 600

MC = 1000 + 100 = 1100

MCL stands for 1000 + 100 + 50 = 1150

3. Third Rule. A symbol of smaller value put on the left of greater value symbol is subtracted from it.

When the smaller numeral is written to the left of a greater numeral, the value of the smaller numeral is subtracted from the greater numeral. The V, L and D are not subtracted. Only one number can be subtracted from another.

For example:

IV stands for 5 - 1 = 4

IX stands for 10 - 1 = 9

XL stands for 50 - 10 = 40

XC stands for 100 - 10 = 90

DC stands for 500 - 100 = 400

Note:

(i) Symbol V, L and D are never subtracted.

(ii) Symbol I can be subtracted from V and X only.

(iii) Symbol X can be subtracted from L and C only as L and C are greater than X.

(iv) Symbol C can be subtracted from D and M.

4. Fourth Rule. A symbol of smaller value, put between two symbols of greater value is subtracted from the symbol on its right.

When the symbols are combined to make a numeral, the value of the symbol between the two symbols is subtracted from the value of the symbol on its right.

For example:

XIV stands for 10 + 5 - 1 = 14

LIX stands for 50 + 10 - 1 = 59

XCIX stands for 90 + 10 - 1 = 99

XLIX stands for 40 + 10 - 1 = 49

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