**High School Number Sense Lesson 17: Converting Roman Numerals to Arabic Numbers**

This concept showed up on over half the tests this year--

**11 times**between

**questions 12 and 19**, inclusive. On high school tests, there weren't any conversions going the other way--from Arabic to Roman numerals. Middle school tests will often include those conversions though.

**Number Dojo Level: 50**

The system of numbers we use today (using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) was developed over 1000 years ago, and the numbers came to be known as Arabic numerals or numbers. Long before, originating in ancient Rome, numbers were represented by letters from the Latin alphabet. In order from smallest to largest, they are:

**I = 1**

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

- The first digit alternates between 1 and 5
- After each pair, a 0 is added to the end.

**typically**from largest to smallest) and adding the values. So, for example:

- MMXVI = 2016 (2 thousands + 1 ten + 1 five +1 one)
- DCIII = 603 (1 five hundred + 1 hundred + 3 ones)
- LXXXVI = 86 (1 fifty + 3 tens + 1 five + 1 one)

**typically**because, to avoid having 4 of the same character in a row, we use

**subtractive notation**as shown here:

- I placed before V or X means 1 less--so 4 is IV (1 less than 5) and 9 is IX (1 less than 10)
- X placed before L or C means 10 less--so XL is 40 (10 less than 50) and XC is 90 (10 less than 100)
- C placed before D or M means 100 less--so CD is 400 (100 less than 500) and CM is 900 (100 less than 1000)

**For example:**

- CXCIII = 193 (C = 100, XC = 90, and III = 3)
- CMXCIX = 999 (CM = 900, XC = 90, and IX = 9)
- MCCXLIV = 1244 (M = 1000, CC = 200, XL = 40, and IV = 4)

**Example 1: CXVI = ___ (Arabic number)**

- C = 100. X = 10. V = 5. I = 1.
- 100 + 10 + 5 + 1 =
**116**.

**Example 2: MDL = ___ (Arabic number)**

- M = 1000. D = 500. L = 50.
- 1000 + 500 + 50 =
**1550**.

**Example 3: XXIX = ___ (Arabic number)**

- XX = 20. IX = 9.
- 20 + 9 =
**29**.

**Example 4: MCDXCII = ___ (Arabic number)**

- M = 1000. CD = 400. XC = 90. II = 2.
- 1000 + 400 + 90 + 2 =
**1492**.

**Example 5: MDCCCLXXXVIII = ___ (Arabic number)**

- M = 1000. D = 500. CCC = 300. L = 50. XXX = 30. V = 5. III = 3.
- 1000 + 500 + 300 + 50 + 30 + 5 + 3 =
**1888**.

**Here's a free worksheet to help you practice RomanToArabic:**

romantoarabic.pdf |

**Up Next for High School: RomanOper**