8.NS.2: Approximating and Comparing Irrational Numbers Using Rational Numbers
Grade: 8th Grade
Domain: NS: The Number System
Standard Description
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
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.