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Roman Numerals (page 2 of 2)


Continuing our counting, we have:

    XV = 10 + 5 = 15
    XVI = 10 + 5 + 1 = 16
    XVII = 10 + 5 + 1 + 1 = 17
    XVIII = 10 + 5 + 1 + 1 + 1 = 18
    XIX = 10 + (10 1) = 10 + 9 = 19
    XX = 10 + 10 = 20

Eventually, we'll get to larger numbers. If we continue using these rules, we can create expressions for whatever values we are given. Let's work some examples.

  • Write 453 in Roman numerals.
  • The biggest numeral smaller than 400 is the C for 100. But I can't do CCCC for the 400, because that's four of the same character in a row. Instead, I have to subtract 100 from 500: CD = 500 100 = 400. Copyright Elizabeth Stapel 2013 All Rights Reserved

    The 50 is easy: that's just L. For the 3, I use three Is. Then my answer is:

      453 = CDLIII

  • Write 1989 in Roman numerals.

 

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Note: This number is one that you might actually see expressed in Roman numerals because, for some reason, the production dates on movies are written in Roman numerals.

    The smallest number-character less than 1900 is 1000: M. After taking care of the thousand, I've got the 900 part of the number. I could start with a D for 500 and then add four Cs for the 400, but I can't use four of the same character in a row. So I'll instead use subtraction to get the 900: one hundred from one thousand is nine hundred, so 900 = CM.

    The next part of the number is the 80; the largest number-character smaller than this is L for 50. Then I'll add three Xs for the three tens: 80 = LXXX. I'm left then with the nine, which is written as "one from ten": IX. Putting it all together, I get:

      1000 + (1000 100) + 50 + 30 + (10 1) = 1989 = MCMLXXXIX

  • You've found an old book with a publication date of "MDCCCXCVII". Express the year in decimal numerals.
  • At the start of this Roman number is M which is 1000. Then comes D which is 500, followed by three Cs which is 300, for a total of 800. Then I've got an X which is 10, but that's followed by another C, which means that the 10 is subracted from 100. In other words, the XC is a 90. After that comes VII which I recognize as being 5 + 1 + 1 = 7.

      The year is 1,000 + 500 + 300 + 90 + 7 = 1897

  • Convert the number 499 from Arabic into Roman numerals.

Interesting fact: Though our letters are Latin (that is, Roman), our numerals came to us through Middle-Ages North Africans; that is, from Arab scholars. So "Arabic numerals" is just a fancy way of saying "the digits we normally use".

    You might think that I could just subtract one from five hundred: ID. But that's too much of a subtraction. In general, I can only subtract 1, 10, or 100 from the next one or two numerals bigger. That is, I can subtract 1 from 10 or 50, but nothing bigger; I can subtract 10 from 50 or 100; and I can subtract 100 from 500 or 1,000, but that's it. (Why? "Because".) So I have to add up to 499, rather than subtracting down from 500.

    The biggest numeral smaller than 499 is 100, but I can't add up to 100 by using four Cs; instead, I have to subtract 100 from 500. This leaves me with the 99. While I can't subtract a 1 from a 100 to get 99, I can subtract a 10 from 100 to get 90. Then I can subtract a 1 from a 10 to get 9. Putting it all together, I get:

      (500 100) + (100 10) + (10 1) = 400 + 90 + 9 = CDXCIX


To summarize:

Roman
numerals

 

Arabic
values

 

permitted
subtractive forms

 

Arabic
values

I

 

1

 

IV

 

5 1 = 4

V

 

5

 

IX

 

10 1 = 9

X

 

10

 

XL

 

50 10 = 40

L

 

50

 

XC

 

100 10 = 90

C

 

100

 

CD

 

500 100 = 400

D

 

500

 

CM

 

1,000 100 = 900

M

 

1,000

 

 

 

 

Always build numbers starting with the biggest-valued character that you can squeeze into the number they've given you, and use subtractive forms wherever you can.

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Cite this article as:

Stapel, Elizabeth. "Roman Numerals." Purplemath. Available from
    http://www.purplemath.com/modules/romannum2.htm. Accessed
 

 



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