3.3.6: Roman Numerals

Last updated
Save as PDF

Page ID: 51820

Amy Lagusker
College of the Canyons

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Why study Roman Numerals?

Even though Roman Numerals are rare in today’s society, they are still used and expected to be understood. They are taught in grades three through five, depending on the district. They can be seen in clocks, the Super Bowl, Film Credits for the copyright date like MCMLXII, preface of textbooks and others like Star Wars Episode VI and WWII.

2.4.1: Basic Table of Roman Numerals
Value	Symbol
1	I
5	V
10	X
50	L
100	C
500	D
1000	M

2.4.2: The Complete Table of Roman Numerals
	1	2	3	4	5	6	7	8	9
ONES	I	II	III	IV	V	VI	VII	VIII	IX
TENS	X	XX	XXX	XL	L	LX	LXX	LXXX	XC
HUNDREDS	C	CC	CCC	CD	D	DC	DCC	DCCC	CM
THOUSANDS	M	MM	MMM	\(\overline{\mathrm{IV}}\)	\(\overline{\mathrm{V}}\)	\(\overline{\mathrm{VI}}\)	\(\overline{\mathrm{VII}}\)	\(\overline{\mathrm{VIII}}\)	\(\overline{\mathrm{IX}}\)
TEN THOUSANDS	\(\bar{X}\)	\(\overline{X X}\)	\(\overline{X X X}\)	\(\overline{X L}\)	\(\bar{L}\)	\(\overline{L X}\)	\(\overline{L X X}\)	\(\overline{L X X X}\)	\(\overline{X C}\)
HUNDRED THOUSANDS	\(\bar{C}\)	\(\overline{C C}\)	\(\overline{C C C}\)	\(\overline{C D}\)	\(\bar{D}\)	\(\overline{D C}\)	\(\overline{D C C}\)	\(\overline{D C C C}\)	\(\overline{C M}\)

Example \(\PageIndex{1}\)

For all numbers except 4 and 9, we ADD the Roman Numerals together, in order from left to right, greatest value to lowest value.

\[\begin{aligned}
11 &=10+1=X I \\
8 &=5+1+1+1=V I I I \\
123 &=100+10+10+1+1+1=C X X I I I \\
3816 &=1000+1000+1000+500+100+100+100+10+5+1=M M M D C C C X V I \\
7002 &=5000+1000+1000+1+1=\overline{V I I }I I
\end{aligned} \nonumber \]

Example \(\PageIndex{2}\)

For any number that includes a 4 or a 9, we subtract. When we are looking at a Roman Number expression and we see a Roman character OUT OF ORDER, which is the clue to SUBTRACT!

\[\begin{array}{l}
9=10-1=I X \\
4=5-1=I V \\
1400=1000+(500-100)=M C D \\
29452=10000+10000+10000-1000+(500-100)+50+1+1=\overline{I X X X} C D L I I
\end{array} \nonumber \]

Partner Activity 1

Convert Between Roman Numerals and Our Current Decimal System:

MMXLV = ________
MDCCLXXXIX = ________
1993 = ______
5495 = ______

Practice Problems

Convert Between Roman Numerals and Our Current Decimal System:

84759
MMXX
MCMLXXXII
1764
50000
\(\overline{X X} L X X X I X\)