Roman Numerals Chapter Notes | Mathematics Class 5 ICSE PDF Download

Introduction

Dive into the fascinating world of Roman numerals, a system crafted by the ancient Romans that’s still used today in clocks, book chapters, and movie sequels! Unlike the numbers we use daily, Roman numerals use special letters to represent values, making them a unique and fun way to explore numbers. In this chapter, we’ll uncover how these symbols work, how to convert between Roman and regular numbers, and even how to do simple math with them. Get ready to step back in time and master this ancient number system!

Roman Numeral System

• Roman numerals were developed by the ancient Romans as one of the earliest number systems.
• It uses seven unique symbols, each with a specific value, to represent numbers.
• The system does not include a symbol for zero.
• Numbers are formed by combining these symbols.
• The seven symbols and their values are:
  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
  • D = 500
  • M = 1,000
• Example: The symbol X represents 10 in the Hindu-Arabic numeral system.

Rules for Writing Hindu-Arabic Numbers Using Roman Numerals

Rule 1

• A Roman numeral can be repeated up to three times in a row.
• When repeated, the values are added together to get the final number.
• Only I, X, C, and M can be repeated; V, L, and D cannot.
• Example: III = 1 + 1 + 1 = 3

Rule 2

• If a smaller value numeral is placed to the right of a larger value numeral, their values are added.
• Example: VI = V + I = 5 + 1 = 6

Rule 3

• If a smaller value numeral is placed to the left of a larger value numeral, the smaller value is subtracted from the larger value.
• V, L, and D cannot be subtracted.
• I can only be subtracted from V and X.
• X can only be subtracted from L and C.
• C can only be subtracted from D and M.
• Example: IV = V - I = 5 - 1 = 4

Rule 4

• If a smaller numeral is between two larger numerals, subtract the smaller numeral’s value from the larger numeral to its right, then add the result to the leftmost numeral.
• Example: XIV = 10 + (5 - 1) = 10 + 4 = 14

Rule 5

• Placing a bar over a Roman numeral multiplies its value by 1,000.
• Example: V̅ = 5 × 1,000 = 5,000

Roman Numerals up to Hundred

• Roman numerals from 1 to 100 follow the rules above to represent numbers.

Writing Roman Numerals Using Hindu-Arabic Numerals

• To convert Hindu-Arabic numbers to Roman numerals, use the rules to combine symbols.
• For numbers like 4 and 9, use subtraction (e.g., IV instead of IIII, IX instead of VIIII).
• For larger numbers, break them into expanded form and convert each part.
• Example: 428 = 400 + 20 + 8 = CD + XX + VIII = CDXXVIII

Addition and Subtraction of Roman Numerals

Steps to add or subtract Roman numerals:

• Convert the Roman numerals to Hindu-Arabic numbers.
• Perform the addition or subtraction.
• Convert the result back to Roman numerals.
• Example: XLV + LXIII = 45 + 63 = 108 = CVIII