8-3 Comparing Real Numbers Objective: Students will be able to compare mathematical expressions involving real numbers. 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. 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. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Do Now:

Algebra 2-1 Rational Numbers on a Number Line Think About The Terms: Whole, Integer & Rational 1) What term(s) could you use to describe −4? 2) What term(s) could you use to describe ? 3) What term(s) could you use to describe ? Harbour

Algebra 2-1 Rational Numbers on a Number Line Challenge What term(s) could you use to describe ? Use the calculator to find what equals to Does it appear to terminate or repeat? Multiply the answer by itself (don’t use the square button). Does the answer equal 8? Harbour

Algebra 2-1 Rational Numbers on a Number Line Harbour

Algebra 2-1 Rational Numbers on a Number Line Name All Sets Of Numbers To Which The Real Number Belongs 0.2525… Harbour

Algebra 2-1 Rational Numbers on a Number Line Which Number Is Greater? Order The Set From Least To Greatest Harbour

On a clear day, the number of miles a person can see to the horizon is about 1.23 times the square root of his or her distance from the ground in feet. Suppose Frida is at the Empire State Building at 1250 feet and Kia is at the Freedom tower at 1362 feet. How much farther can Kia see than Frida?

Worksheets Homework 8-3 Pages 93-94 All #’s

Give an example of each of the following: Exit Ticket: Give an example of each of the following: A whole number, an integer that is not a whole number, a rational number that is not an integer and an irrational number.