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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.

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:

 Romannumerals Arabicvalues permittedsubtractive forms Arabicvalues 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.

 Cite this article as: Stapel, Elizabeth. "Roman Numerals." Purplemath. Available from     http://www.purplemath.com/modules/romannum2.htm. Accessed [Date] [Month] 2016

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