Class 5 Notes - Numerals

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Numerals are symbols or a set of symbols used to represent numbers. In this chapter, we will learn about the different numeral systems, their representations, and their applications in mathematics and daily life.

Types of Numerals

Numerals can be categorized into different types based on the system or base they use. The most common numeral systems are:

  • Hindu-Arabic Numerals: The numeral system we use in daily life, consisting of 10 digits (0-9).
  • Roman Numerals: An ancient numeral system using letters like I, V, X, L, C, D, and M.
  • Binary Numerals: A base-2 numeral system using only 0 and 1, widely used in computing.

The Hindu-Arabic Numeral System

This is a positional numeral system that uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit's position in a number represents its value based on powers of 10.

Place Values

In the Hindu-Arabic system, the place value of a digit depends on its position:

  • Units (1)
  • Tens (10)
  • Hundreds (100)
  • Thousands (1000)
  • Ten Thousands (10,000)
  • And so on...

Example: In the number 4,567:

  • 4 is in the Thousands place (4 × 1000 = 4000)
  • 5 is in the Hundreds place (5 × 100 = 500)
  • 6 is in the Tens place (6 × 10 = 60)
  • 7 is in the Units place (7 × 1 = 7)

Roman Numerals

Roman numerals use combinations of letters to represent numbers. Here are the basic symbols:

  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
  • D = 500
  • M = 1000

Rules for Roman Numerals

  • A smaller numeral before a larger numeral means subtraction (e.g., IV = 4).
  • A smaller numeral after a larger numeral means addition (e.g., VI = 6).
  • A numeral can be repeated up to three times to represent addition (e.g., III = 3).

Example: Convert 1987 to Roman numerals:

1987 = 1000 + 900 + 80 + 7 = M + CM + LXXX + VII = MCMLXXXVII

Binary Numerals

The binary numeral system is a base-2 system that uses only two digits: 0 and 1. Each position represents a power of 2.

Place Values in Binary

The place values in binary are as follows:

  • 20 = 1
  • 21 = 2
  • 22 = 4
  • 23 = 8
  • And so on...

Example: Convert the binary number 1011 to decimal:

  • 1 × 23 = 8
  • 0 × 22 = 0
  • 1 × 21 = 2
  • 1 × 20 = 1

Total = 8 + 0 + 2 + 1 = 11

Comparison of Numeral Systems

Each numeral system has its unique features and applications:

  • Hindu-Arabic numerals are widely used in daily life for calculations.
  • Roman numerals are often used in clocks, book chapters, and historical documents.
  • Binary numerals are essential in computer systems and digital electronics.

Practice Problems

  1. Write the Hindu-Arabic numerals for the Roman numerals: XII, XXIX, and XLIV.
  2. Convert the binary numbers 1101 and 10101 to decimal.
  3. Write the expanded form of the number 7,304.
  4. What is the place value of 5 in the number 5,678?

Summary

Numerals are fundamental to mathematics and daily life. By understanding different numeral systems and their properties, we can perform a variety of calculations and represent numbers in different ways. This chapter introduced the Hindu-Arabic, Roman, and Binary numeral systems, along with their applications and rules.