Let's study the Roman numerals an
alternative enumeration system that was
invented by the ancient Romans and is
still used nowadays
for some applications. It is used in the cinema
to number the episodes of Star Wars.
In the 70s and 80s were the episodes 4,
IV, 5, V, and 6, V I.
It started with episode 4, because there were three episodes happening in the past that was
output later. There were the episode 1, I,
the episode 2, II, and the episode 3, III.
The episode 7 is after the episode 6: 7,
VII, 8, VIII, 9, IX.
What are the first Roman numerals? They are fistful on fingers, 1, 2, 3, 4, 5.
The 5 first Roman numerals are constructed with the symbols I for one and V for 5.
Then we use additions and subtractions between 1 and 5.  II is I plus I, 1 plus 1, 2 III is I plus I plus I,
1 plus 1 plus 1, 3, and IV, with the I
before the V of 5, it is V minus I,
and it is 4 because it is 5 minus 1.
What are the five next Roman numerals?
We use for 1, V 4 5, and X fot 10. And then we continue to use additions and
subtractions between 6 and 10. V I is V
Plus I, 5 plus 1, 6.
VII is V plu I plus I, 5 + 1 + 1, 7, VIII
is V + I + I + I,  5 + 1 + 1 + 1 8
IX, with an I in front of the X, it
is X - I ,10 - 1, 9.
Let's continue with the Roman numerals from 11 to 39. These Roman numerals are based on the symbols
I for 1, V for 5, and X for 10. And we
continue to use additions and
subtractions for all the numbers between
11 and 39. X I is X+I, 10 + 1, 11.
X V is X plus V, 10 + 5, 15. X I X it is X plus IX, that is X minus I so it is
10 plus 10 minus 1 that is 19
XX IV is XX, X plus X, plus IV, V minus I.
So it is 10 plus 10, 20, plus 5 minus 1, 4,
that is 24. XXXIX is XXX, X plus
X plus X, plus IX, X minus I,
that is 10 plus 10 plus 10, 30, plus 10 minus 1, 9, that is 3.
Now we continue, from 40 to 89. I is for 1, V is for 5, X is for 10, and L is for 0.
Then we continue to use a additions and subtractions for the numbers
between forty and eighty nine. XL is L
minus X, that is 40, 50 minus L.
XLIX is L minus X plus X minus I, that is
50 minus 10, 40, plus 10 minus 1, 9,
That is 49. LVIII is L plus V plus I plus I
plus I that is 50 plus 5 plus 1 plus
1 plus 1, that is 58. And LXXVII is
L plus X plus X, plus V plus I plus I,
that is 50 plus ten plus ten, seventy,
plus five plus one plus one, seven,
that is 77. And LXXXIX
is L plus X plus X plus X plus X,
plus X minus I, that is 50 plus 10 plus 10 plus ten eighty plus 10 minus 1 that is 89.
And now, we see the whole Roman numerals system: it doesn't go very far!
I for one, V for five, X for 10, L for50, C
for 100, D for 500,
and L for 1,000. It doesn't go further. XC is
490 because it is 100 minus 10. C minus X.
XCIV is a CD, 500 - 100, plus XC, 50 minus
10, plus IV, 5 minus 1. This is 444.
And MMXX is for the year 2020, 1000 plus 1000 + 10 + 10, and the 21st century is written XXI Century.
And the biggest number in Roman numerals is MMM, 3000, CM, 1000
minus 100, 900, XC, 100 minus ten, ninety, IX, 10 - 1, 9. That is 3,999, not further.
The Roman numeral system
follows strict rules that we give here.
the symbols are first ordered: I for one
is less than V for 5, that is less than X for 10,
that is less than L for
50, that is less than C for 100,
that is less than D for 500, that is less than M for 1000.
To write a number between one and 3,999 we write the symbols in decreasing order from left to right.
The symbols I, X, C and M may
be repeated two or three times.
The symbols I, X, and C may be put in front of a larger symbol: that larger symbol may be
V or X for I, L or C for X, and D or M for C.
A number in Roman digits is read from left to right.
The repeated symbols are grouped, and their value is multiplied
by their number (f there are two of them,
it is multiplied by two). If a smaller
symbol is in front of larger one they
are grouped and the smaller is
subtracted to the larger one. For
instance, IV is five minus one.
Then either the isolated symbol or the
groups are added together.
And now let's see some examples. First example: write 1968 in Roman numerals.
We first decompose it as a sum: it is equal to 1000 plus 900 plus 60 plus 8.
Then the terms are subdivided further: 1000 is okay, 900 is 1000 minus 1, 60 is 50 plus 10,
and 8 is 5 plus 1 plus 1 plus 1.
And then we write the number: MCM M is for 1000, CM is for 900, and VIII
is for 8.
Second example: read the number that writes MMXLVII, in the roman numeral system.
First read the number from left to right:
MMXLVII. Group the two M’s together,
to get two times 1,000, that is 2,000. Group X and the L together,
to get 50 minus 10 that is 40.
And group the two I’s together to get 2
times 1 that is 2.
Add all the symbols and groups together:
2,000 plus 40 plus five plus two is
equal to 2,047.
This is the end of our video about the
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