roman numerals

Have you read about King Henry \(VI\), Queen Elizabeth \(II\) in history books?

Have you watched movies like Mission Impossible \(II\), Jurassic Park \(III\), Men in Black \( II\), and Blade \(II\)? 

Do you wonder what do these symbols \(VI\), \(II\), \(III\) mean after the names of kings, queens, popes, books, or movie titles?

These are Roman Numerals. Though not used very often today it would be a good idea to understand the roman representation of numbers.

In this lesson, we will 

• Define roman numeral
• Explain the rules of the roman numeral
• Describe how to change a whole number to the roman numeral and vice versa

Roman Numerals were used by the Ancient Romans as their numbering system. Roman numerals are still used in certain places today.

Roman numerals use letters instead of numbers. There is no 0 in Roman numerals.

There are seven letters you need to know:

\(1 = I\)

\(5 = V\)

\(10 = X\)

\(50 = L \)

\(100 = C\)

\(500 = D\)

\(1000 = M\)

You put the letters together to make numbers. Look at a few simple examples:

\(III = 3\)

Three I’s together is three 1’s and 1 + 1 + 1 equals 3

\(XVI = 16\)

⇒ 10 + 5 + 1 = 16

These examples were simple, but there are a few rules and a few tricky things to know when using Roman numerals.

1. The first rule just says that you add letters, or numbers if they come after a bigger letter or number. For example, XVII = 17. The \(V\) is less than the \(X\), so we added it to the number;\( I\) was less than the \(V\), so we added the two \( I\) to the number.

2. The second rule is that you can’t put more than three letters together in a row. For example, you can put three I’s together, III, to make a 3 but you can’t put four I’s together (like \(IIII\)) to make a four. How do you make a 4 then? See the next rule.

3. You can subtract a number by putting a letter of lower value before one of higher value.

This is how we make the numbers four, nine, and ninety.

• \(IV\) = \(5 -1 = 4\)
• \(IX\) = \(10 -1 = 9\)
• \(XC \)= \(100 - 10 = 90\)

There are a few restrictions on when you can do this:

• You can only subtract one number. You can’t get a 3 by writing \( IIV\)
• You can only do this with \(I, X,\) and \(C\). Not with \(V, L,\) or \(D\).
• The smaller subtracted letter must be either 1/5^th or 1/10^th of the larger one. For example, 99 cannot be written \(IC\) because \(I \) is 1/100^th of \(C\).

4. The last rule is that you can put a bar over a number to multiply it by a thousand and make a really big number.

For example, the numbers 1 through 10:

I, II, III, IV, V, VI, VII, VIII, IX, X

The tens (10, 20, 30, 40, 50, 60, 70, 80, 90, 100):

\(X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C\)

Using roman numerals to write years

It is very easy to write a number as a Roman numeral. For example, let's take year 1984. We first expand it like below

1984 = 1000 + 900 + 80 + 4 

Now, 

\(1000 = M\)

\(900 = CM (1000-100)\)

\(80 = LXXX\) (\(L = 50\) and \(XXX = 10 + 10 + 10 = 30\))

\(4 = IV (5-1)\)

Adding all of these

1984 = 1000 + 900 + 80 + 4 = \(M + CM + LXXX + IV = MCMLXXXIV\)

Getting the number from the roman numeral is equally simple, by adding the values of the symbols.

 

Let's see some more examples of large numbers as in representing a year: 

• 1994

First, we expand it as per place values:

1000 + 900 + 90 + 4 

\(M\) for 1000

\(CM\) for 900 (1000 - 100)

90 becomes 100 - 10 = \(XC\) (because as per the rule we can’t put more than three letters together in a row)

4 = 5 - 1 = \(IV\)

Therefore, 1994 = 1000 + 900 + 90 + 4 = \(M + CM + XC + IV = MCMXCIV\)

 

• 1776

1000 + 700 + 70 + 6 

1000 is \(M\)

700 = 500 + 100 + 100 = \(D + C + C = DCC\)

70 =  50 + 10 + 10 = \( L + X + X = LXX\)

6 = 5 + 1 = \(VI\)

Therefore, 1776 = 1000 + 500 + 100 + 100 + 50 + 10 + 10 + 5 + 1

= \(M + DCC + LXX + VI = MDCCLXXVI\)

 

• 1492

1000 + 400 + 90 + 2

= 1000 + (500 - 100) + (100-10) + 1 + 1

= \(M + CD + XC + I + I\)

= \(MCDXCII\)