Know that there are numbers that are not rational, and approximate them by rational numbers. 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., ?2). 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.
Supports the following Standards of Mathematical Practice
• 2 Reason abstractly and quantitatively. • 5 Use appropriate tools strategically. • 6 Attend to precision. • 7 Look for and make use of structure. • 8 Look for and express regularity in repeated reasoning.