Lesson 1.1: Classifying Rational Numbers

Rational Numbers

• Defined as numbers that can be expressed as a fraction.
• Includes decimals that either terminate or repeat with a pattern.

Integers

• Comprise positive and negative whole numbers, including zero.
• Do not include fractions or decimals.

Whole Numbers

• Any positive number, including zero.
• Excludes fractions and decimals.

Natural Numbers

• Positive numbers that don't have fractions or decimals, starting from one.
• Also referred to as counting numbers.

Classification of Numbers

• 36: Classifies as rational, integer, whole, and natural.
• -29: Classifies as rational and integer only.
• -2.6: A rational number.
• 0: Classifies as rational, integer, and whole.

True/False Statements Analysis

• Not all rational numbers are whole numbers (e.g., rational numbers can include fractions).
• All whole numbers are rational numbers, as they can be expressed as fractions (e.g., 5/1).
• Some integers are also whole numbers (e.g., 5).
• Not all integers are whole numbers (e.g., -5).
• All natural numbers are rational numbers, being subsets of them.
• Not all rational numbers are natural numbers (e.g., 2.5).
• Some integers are natural numbers (e.g., 3).
• All natural numbers are integers, consisting solely of non-negative whole numbers.
• Not all whole numbers are natural numbers due to the inclusion of zero.
• All natural numbers fit within the whole numbers classification.

Summary of Relationships

• Whole numbers are a subset of rational numbers.
• Rational numbers encompass integers, while integers consist of both whole numbers and negative numbers.