1.2: Rational and Irrational Number Properties

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Presentation transcript:

1.2: Rational and Irrational Number Properties Objective: To identify and define rational and irrational properties.

Do Now: Real numbers are numbers that are not imaginary. These numbers can be grouped into two major classifications: rational and irrational. Rational numbers: A real number that can be written as a ratio of two integers. Irrational numbers: A real number that cannot be written as a ratio of two numbers. Using the above definitions, determine in your group if your flashcards are rational or an irrational. Be prepared to explain why.

Calculator tutorial Radical: 2nd , x2 Cube root: MATH, 4 Squaring a number: x2 Raising a number to a power: ^ Absolute Value: MATH, , ENTER Fraction: ALPHA, Y1, ENTER Pi: π

Answers: Rational Numbers Irrational Numbers 1 2 1.75 -4.2 16 −2.4 10 3 3 8 3 𝜋 7𝜋 5 − 6 2 0.707106… 𝜋 4 3 12

Types Rational Numbers Repeating decimals Terminating decimals Fractions Whole numbers Integers Natural Numbers Repeating decimals Terminating decimals Fractions

Types Irrational Numbers Non-repeating, non-terminating decimals Non-repeating, non-terminating decimals

Think About It: With a partner state the scientific method.

Properties We can use the scientific method to determine whether or not the following statements are true. On the next slide there will be a list of statements. You must determine if they are true or false. By experimenting with rational and irrational numbers within a group. For each statement, you must try three different pairs of numbers. You may use a calculator. You will be broken into groups and assigned a few statements to prove true or false. After you are given time to work out the solutions, you will have to present your findings to the class.

The sum of two odd numbers is even. Examples: Hypothesis Work True or False 1. The sum of two odd numbers is even. 3+7=10 5+15=20 31+9=40 All the sums are even. TRUE The sum of two odd numbers is even. 2. The product of an even and odd number is odd.

Statements The sum of two rational numbers is rational. The product of two rational numbers is irrational. The difference of two rational numbers is rational. The quotient of two rational numbers is irrational. The sum of two irrational numbers is rational. The product of two irrational numbers is irrational. The difference of two irrational numbers is rational. The quotient of two irrational numbers is irrational. The sum of a rational and irrational number is rational. The difference of an irrational and rational number is irrational. The product of a rational and irrational number is rational. The quotient of a rational and irrational number is irrational.

Regents Practice: