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Name________________________________________Date______________8 th Grade Aim What are rational and irrational numbers? Warm up Plot a point to graph each of the following numbers on the number line below. -2.5 16 800% 28 1 1 3 81 Whole Group Questions Rational Numbers can be written as decimals and fractions. Irrational Numbers cannot be written as a fraction. They are non-terminating and non-repeating. 1. Before 8th grade, every number you have ever seen is rational except _______. 2. Now every number you see is rational except _______ and the square roots of _________________________________. 3. Which number in the Warm Up was irrational? Irrational numbers are decimals that never end, but they don’t repeat either. This means they cannot be written as fractions. All fractions convert to decimals that either end or repeat. (Decimals that end actually have a repeating pattern of zeros.) Examples of Rational Numbers 1. Use a calculator to convert these fractions to terminating decimals. a. 2. 1 4 b. 1 10 Use a calculator to convert these fractions to repeating decimals. a. 1 3 b. 21 99 Examples of Irrational Numbers 3. Use a calculator to convert these numbers to decimals that go on forever with no pattern. a. 22 b. 99 c. 4. Circle the irrational numbers below. 3 5 13 3 2 3 -7 1 2 25 2 Group Work 1. Circle the irrational numbers below. 3 4 4 24 4 9 1 5 10 9 3.14 -10 64 2. Square roots of non-perfect squares and have ever seen are rational. are irrational. All other numbers you The number sets below are all examples of different types of rational numbers. Fill in each blank with the appropriate vocabulary term. A. The set of _____________ are the numbers you first learned to count with as a child. They are also called natural numbers. ex. B. The set of _____________ includes all of the counting numbers and zero. ex. C. {0, 1, 2, 3, … } The set of _____________ includes all of the whole numbers and their opposites. ex. 3. {1, 2, 3, …} {…, -3, -2, -1, 0, 1, 2, 3, …} D. _____________ are numbers that consist of an integer and a fraction or decimal. ex. 5 1 10 -2 3 4 6.4 Tell which number below is rational and which number is irrational. Use definitions to support your answer and include the value or approximate value of each number in your answer. 4 6