Topic 1: Know that there are numbers that are not rational and approximate them by rational numbers. September 16/17 Essential Question: How can I identify rational numbers using decimal expansion? Questions Notes 1. A rational number is a number that can be written as a fraction or a decimal that terminates or repeats. 2. A terminating decimal is a decimal that ends Examples: 1.8 -­‐0.04 0.25 5.0 3. A repeating decimal is a decimal that repeats the same number or group of numbers forever. A bar indicates the repeated digit. Examples: 0.3333 … = 0. 3 −0.44444 … = −0. 4 0.466666 = 0.46 1.484848 = 1. 48 Summary: September 18 Essential Question: How are irrational numbers related to rational numbers? Questions Notes 1. An irrational number is a number that cannot be written as a fraction. 2. A decimal is an irrational number if the numbers do not repeat and the numbers go on forever (does not terminate). 3. Common Irrational Numbers o 𝜋 , Pi! o 𝜋 = 3.141592654 … 𝜋 ≈ 3.14 o Imperfect Square Roots √12 = 3.464101615137754 … √12 ≈ 3.5 o Imperfect Cube Roots ∛12 = 2.289428485106664 … ∛12 ≈ 2.3 4. In order to use irrational numbers in math problems we find and use an approximate value of the irrational number. The approximated value of an irrational number becomes a rational number. Summary: