8.NS.1: Understanding Rational and Irrational Numbers and Their Decimal Expansions
Grade: 8th Grade
Domain: NS: The Number System
Standard Description
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Domain Description
Understand that irrational numbers are distinct from rational numbers due to their non-repeating decimal expansion. Demonstrate this by turning repeating decimals into rational numbers. Utilize rational equivalents of irrational numbers to analyze their size, pinpoint their approximate location on a number line, and gauge the worth of expressions (like π2). Illustrate this using √2's decimal truncation by indicating that its value falls between 1 and 2, then between 1.4 and 1.5, and providing instructions for deriving more accurate estimations.