**Category : ** *
5th Class
*

**ROMAN NUMBER**

** FUNDAMENTALS**

- The system of Numeration, developed by Romans is called the Roman numerals system. In Roman numerals system there are seven distinct symbols. viz I, V, X, L, C, D and M.

Roman symbols and their corresponding Hindu-Arabic numbers

Roman Numerals |
I |
V |
X |
L |
C |
D |
M |

Hindu-Arabic Numerals |
1 |
5 |
10 |
50 |
100 |
500 |
1000 |

** Roman numerals formation rules**

- If a symbol in roman numeral system is repeated, its value is added as many times as it appears.

Example: \[II=1+1=2\]

\[XXX=10+10+10=30\]

\[CC=100+100=200\]

\[MMM=1000+1000+1000=3000\]

It may be noted that no numerals can be repeated more than 3 times. Repetition is allowed only for symbols I, X and C.

V, L and D are never repeated

- A symbols of small value is placed to the right of larger value and its value is added to the larger value.

Example:

\[XII=10+1+1=12\]

\[XV=10+5=15\]

\[LV=50+5=55\]

\[CX=100+10=110\]

- A symbol of smaller value is placed to the left of larger value and its value is subtracted from the larger value.

Example:

\[IV=51=4\]

\[IX=91=8\]

\[VL=505=45\]

\[VC=1005=95\]

\[XC=10010=90\]

- The symbol V (5), L (50) and D (500) can?t be placed to the left of larger value. i.e. V, L and D are never subtracted.
- A symbol of smaller value is placed between two symbols of larger value. It is always subtracted from the immediately following symbol of larger value.

Example: \[XIV=10+(5-1)=14\]

\[XXIV=10+10+(5-1)=24\]

\[CXL=100+(5010)=140\]

If a bar is placed over a symbol in a Roman numeral system, its value is multiplied by 1000.

Example:\[\overline{V}=5000\]

\[\overline{L}=50000\]

\[\overline{C}=100000\]

- A symbol can be repeated up to a maximum of three times only.
- I can be subtracted from V and X only.
- X can be subtracted from L and C only.
- C can be subtracted from D and M only.

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