Lesson 21: Roman Numerals

Introduction to Roman Numerals

Hello, young mathematicians! We use numbers like $1, 2, 3, 4,$ and so on every day. These are called **Hindu-Arabic numerals**. But did you know there's another way to write numbers that was used a long, long time ago by the ancient Romans? These are called **Roman numerals**!

You might have seen Roman numerals on old clocks, in chapter numbers of books, or even on movie titles! They use letters from the alphabet to represent values.

Let's learn how to read and write these interesting numbers!

Basic Roman Numerals and Their Values

There are seven basic symbols in Roman numerals:

Rules for Forming Roman Numerals

To form other numbers, we combine these symbols using a few rules:

• Repetition: A symbol can be repeated up to three times to add its value (e.g., II = $1+1=2$, XXX = $10+10+10=30$). V, L, and D are never repeated.
• Addition: If a smaller value symbol is placed *after* a larger value symbol, we add their values (e.g., VI = $5+1=6$, LX = $50+10=60$).
• Subtraction: If a smaller value symbol is placed *before* a larger value symbol, we subtract the smaller from the larger (e.g., IV = $5-1=4$, IX = $10-1=9$). Only I, X, and C can be subtracted.
  • I can be subtracted from V and X.
  • X can be subtracted from L and C.
  • C can be subtracted from D and M.
• No more than three repetitions: For example, $4$ is IV, not IIII. $9$ is IX, not VIIII.

Converting Roman Numerals to Standard Numbers

To convert, read the Roman numeral from left to right, applying the addition and subtraction rules.

Exercise 1: Convert the following Roman numerals to standard numbers.

Converting Standard Numbers to Roman Numerals

To convert a standard number to Roman numerals, break it down into thousands, hundreds, tens, and ones, and then convert each part.

Exercise 2: Convert the following standard numbers to Roman numerals.