Know that there are numbers that are not rational, and approximate them by rational numbers: 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.
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.