Welcome to a lesson on Roman numerals.
Roman numerals, the numeric system in ancient Rome,
uses combinations of letters from the Latin alphabet
to signify values.
Here we have the Roman numerals on the left
and the Arabic numerals on the right.
Many numbers are formed by combining symbols together
and placed from left to right in order of value.
Notice in this first example, we have two capital Is,
each of which are equal to one,
so we add these one plus one is equal to two.
Here we have a V followed by three capital Is,
this would be five plus three, which is equal to eight.
Notice how we're adding these
and these are ordered from greatest value to least value.
Next we have two Xs, that would be 10 plus 10 or 20,
plus V followed by I, which would be five plus one, or six.
This is 26.
Next, we have an L, which is equal to 50.
And X is 10, 50 plus 10 would be 60.
Plus the V, which is equal to five, 60 plus five is 65.
Next we have C, which is 100,
and then we have L followed by X,
that would be 50 plus 10, that's 60,
plus V followed by I, that would be five plus one, or six.
This 166.
Next we have D, which is 500, followed by two Cs,
that would be 500 plus 100 plus 100, or 700,
plus V followed by I, which is six, so this is 706.
Here we have two capital Ms,
that would be 1,000 plus 1,000, or 2,000,
plus D followed by C, that's going to be 500 plus 100,
that's 600, plus X, which is 10, plus two capital Is,
that's two, this would be 2,612.
Now, to avoid four repeated characters,
if a smaller numeral comes before a larger numeral,
the smaller is subtracted from the larger.
So, for example, here, notice how
the I is smaller than the V, because I is one and V is five.
Therefore, this is five minus one, or four.
We represent four this way instead of four capital Is,
to avoid four repeated characters.
Next, we have an I before an X,
which is a one before a 10, so this would be 10 minus one,
or nine.
Next we have an X before an L,
where the X is 10 and the L is 50,
so this would be 50 minus 10, or 40.
Here, we have an X before a C,
where the X is 10 and the C is 100,
so this is 100 minus 10, that'd be 90, plus V followed by I.
Notice how the smaller value's to the right, so we add.
This is five plus one, or six.
So, this is 96.
Next, we have a C before a D, that would be 500 minus 100,
or 400 plus an X before an L, that would be 50 minus 10,
or 40, plus an I before a V, that's five minus one,
or four.
So, we have 444.
Next, we have two capital Ms, that's 2,000,
plus, we have X before C, that would be 100 minus 10,
or 90, plus V, which is five, would be 2,095.
Then finally, we have a C before M,
that would be 1,000 minus 100 or 900.
Plus X before L, that would be 50 minus 10, that's 40,
plus an I before an X, that would be 10 minus one, or nine.
This is 949.
Now, the subtraction principle can be a little tricky
because there are restrictions on the subtractive principle
for Roman numerals.
You can only subtract a power of 10 and only
from the next higher digits where the digits
are I, V, X, L, C, D and M.
That is, only I, X and C can be subtracted
and I can be subtracted only from V and X,
where X can only be subtracted from L and C,
and C can only be subtracted from D and M.
So, the subtracting principle can get a little tricky.
Let's take a look at some examples of forming
Roman numerals from the Arabic numerals.
So, for 37, we'll start with a 30,
that would be three Xs, and then for seven,
we would have a V followed by two Is.
For 49, we will use the subtraction principle,
but we can't use an I and an L.
We'll start with the 40, by putting an X before the L,
that would be 50 minus 10.
So, we'll use XL, that's 40, and then for nine,
we'll use an I before an X, for 10 minus one.
So, here's 49.
For 236, we'll start with 200, which is two Cs.
For 30, we'll use three Xs, and then for six,
we'll use a V followed by an I.
For 475, we'll start with 400, we'll have to use
the subtraction principle.
We'll put a C before the D, for 500 minus 100.
So there's 400.
And then for 70, we'll use 50 plus 10 plus 10
or LXX, for five, we use a V.
Next, for 1,241, we M for 1,000, two Cs for 200,
now for 40, we'll have to use an X before an L.
So there's 50 minus 10, that's 40 and there's the one.
And now for 989, we'll start with the 900
by using a C before an M, this would be 1,000 minus 100.
For 80, we will use a 50 and three 10s, or LXXX,
for nine, we'll an I before an X for 10 minus one.
Finally, for 3,993, we'll use Ms for 3,000.
And now for 900, we'll use a C before an M
for 1,000 minus 100.
And then for 90, we'll use an X before a C
for 100 minus 10.
And then for three we have three capital Is.
Now, there's one more thing to mention before we go.
Roman numerals may be written as lower case letters,
but it is more common to use upper case letters.
But here are the Roman numerals using lower case letters
for reference.
I hope you found this lesson helpful.