Irrational? Why or Why Not? What are the characteristics of irrational numbers? After completing this lesson, you should be able to know that numbers that are not rational are called irrational. You will understand that every number has a decimal expansion. Irrational numbers have characteristics that classify them as irrational.

8th Grade Math Standards M.8.NS.1- 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. M.8.NS.2- 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. The 8th grade math standards addressed in this lesson include the following: M.8.NS.1- 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. You will also: M.8.NS.2- 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.

Do not terminate Do not repeat Are not predictable Irrational Numbers… Do not terminate Do not repeat Are not predictable Irrational numbers do not terminate in decimal expansion Irrational numbers do not repeat when in decimal expansion. Irrational numbers do are not predictable in decimal expansion.

Examples of Irrational Numbers: ∏ = 3.141592653589793… √2 = 1.414213562373095… √3 = 1.732050807568877… Pi is an irrational number. When pi is in decimal expansion the values do not terminate and do not have a repeating pattern. √2 and √3 are also examples of irrational numbers because they too do not terminate and do not have a repeating pattern. Pi, √2 and √3 all numbers that can only be approximated when graphing on the number line.

Graph: ∏ = 3.141592653589793… √2 = 1.414213562373095… √3 = 1.732050807568877… ∏ √2 √3 You must use rational numbers as a guide to graph irrational approximations when graphing on a number line.

Get ready to begin your journey exploring the 8th grade math lessons in this unit. You will be able to “Reach for the Stars” before you know it! Reach for the Stars !