Classifying Numbers in Mathematics

Classification of Numbers

• Natural Numbers: 1, 2, 3, ... (positive integers)
• Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
• Rational Numbers: fractions (e.g. 3/4, 22/7) and decimals (e.g. 0.5, 3.14)
• Irrational Numbers: non-repeating, non-terminating decimals (e.g. π, e)
• Real Numbers: includes rational and irrational numbers
• Complex Numbers: numbers with both real and imaginary parts (e.g. 3 + 4i)

Properties of Numbers

• Commutative Property: the order of numbers does not change the result (e.g. 2 + 3 = 3 + 2)
• Associative Property: the order in which numbers are grouped does not change the result (e.g. (2 + 3) + 4 = 2 + (3 + 4))
• Distributive Property: numbers can be distributed across addition and subtraction (e.g. 2(3 + 4) = 2(3) + 2(4))

Types of Number Operations

• Arithmetic Operations:
  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
• Exponentiation: raising a number to a power (e.g. 2^3, 5^2)
• Roots: finding the root of a number (e.g. √4, ∛8)

Important Number Concepts

• Place Value: the value of a digit based on its position in a number (e.g. hundreds, tens, ones)
• Rounding: approximating a number to a specified number of decimal places
• Significant Figures: the number of digits in a number that are known to be reliable
• Percentages: a way to express a value as a fraction of 100 (e.g. 25% = 1/4)

Classification of Numbers

• Natural Numbers are positive integers, starting from 1.
• Whole Numbers are non-negative integers, including 0.
• Integers are whole numbers, both positive and negative.
• Rational Numbers are fractions and decimals that can be expressed as a finite decimal or a ratio of integers.
• Irrational Numbers are non-repeating, non-terminating decimals.
• Real Numbers include both rational and irrational numbers.
• Complex Numbers have both real and imaginary parts.

Properties of Numbers

• The Commutative Property states that the order of numbers does not change the result of an operation.
• The Associative Property states that the order in which numbers are grouped does not change the result.
• The Distributive Property allows numbers to be distributed across addition and subtraction operations.

Types of Number Operations

• Arithmetic Operations include addition, subtraction, multiplication, and division.
• Exponentiation involves raising a number to a power.
• Roots involve finding the root of a number.

Important Number Concepts

• Place Value is the value of a digit based on its position in a number.
• Rounding involves approximating a number to a specified number of decimal places.
• Significant Figures are the number of digits in a number that are known to be reliable.
• Percentages are a way to express a value as a fraction of 100.