2.4: Roman Numerals
- Page ID
- 50989
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
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.
Value | Symbol |
---|---|
1 |
I |
5 |
V |
10 |
X |
50 |
L |
100 |
C |
500 |
D |
1000 |
M |
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
- \(\overline{X X} L X X X I X\)