Lesson 9.2 Rational and Irrational Numbers

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Presentation transcript:

Lesson 9.2 Rational and Irrational Numbers Essential Question: How do you classify and order rational and irrational numbers?

Before we start… If you have 3 4 of a dollar, how much money do you have?

What is a rational number? A rational number can be written as a fraction,

What is an irrational number? Cannot be written as a quotient of two integers (fraction); its decimal neither terminates nor repeats

What are the real numbers? The set of all rational and irrational numbers. Every point on a real number line is a real number.

Real Numbers Rational Numbers Irrational Numbers Fractions Terminating decimals Repeating decimals Integers Whole numbers Irrational Numbers Can’t be written as a fraction Decimals that don’t terminate or repeat

Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers

How do you classify real numbers? If the number can be written as a fraction, it’s rational. If it can’t be written as a fraction, it’s irrational.

Classify the numbers

Classify the numbers

Classify the numbers 3 4 7

How do you compare real numbers? You can graph the numbers on a number line using approximations for square roots or you can convert all numbers to decimals.

Order the numbers from least to greatest and then classify. − 2 3 , −0.6, −1, 1 3

Order the numbers from least to greatest and then classify. 0.4 7 , 0. 474 , 0. 47 , 0.23

Order the numbers from least to greatest and then classify. 1.7, 1.7 , 1. 89 , 1. 3

Waves For large ocean waves, the wind speed s in knots and the height of the waves h in feet are related by the equation 𝑠= ℎ 0.019 . If the waves are about 9.5 feet tall, what must the wind speed be?

Distance The equation 𝑑= 3ℎ 2 models the distance d in miles that a person can see to the horizon from an eye-level height of h feet above the ground. If a woman stands with a normal eye-level of 5 feet stands on a cliff 100 feet high, how far can she see to the horizon?

How do you classify and order rational and irrational numbers?

Ticket Out the Door Order the numbers from least to greatest. Place your name on the paper and place it in the basket. 49 , 8, − 4 , 4 7 , −3, 7