1-3 Real Numbers and the Number Line
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Transcript of 1-3 Real Numbers and the Number Line
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1-3 Real Numbers and the Number Line
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The radical symbol indicates a nonnegative square root
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
√81
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
√ 916
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
√64
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression
√ 136
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The square of an integer is called a perfect square. 49 is a perfect square because is a perfect square.
When a radicand is not a perfect square, you can estimate the square root.
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Problem 2: Estimating a Square Root
Lobster eyes are made of tiny square regions. Under a microscope, the surface of the eye looks like graph
paper. A scientist measures the area of one of the squares to be 386 square
microns. What is the approximate side of the square to the nearest micron?
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Problem 2: Estimating a Square Root
What is the value of to the nearest integer
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Problem 4: Comparing Real Numbers
Inequality: a mathematical sentence that compares the values of two expressions using an inequality symbol.< LESS THAN> GREATER THAN LESS THAN OR EQUAL TO GREATER THAN OR EQUAL TO
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What is an inequality that compares
What is an inequality that compares
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Problem 5: Graphing and Ordering Real Numbers
What is the order of from least to greatest. Then order on a number line.
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Problem 5: Graphing and Ordering Real Numbers
What is the order of from least to greatest. Then order on a number line.
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Problem 3: Classifying Real
Number
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Rational Number: In the form , where a and b are integers and In decimal form they are terminating decimal such as 5.45 or a repeating decimal such as 0.416666… which you can write as
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Natural numbers: also called counting numbers and are the ones you count with {1, 2, 3, …}
Whole Numbers: include the natural numbers, but also includes zero {0, 1, 2, 3, …}
Integers: The whole numbers, plus their respective negative numbers {…, -3, -2, -1, 0, 1, 2, 3, …}
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Irrational numbers: cannot be written as a fraction. In decimal form, irrational numbers do not terminate or repeat.
(some square roots are rational and some are irrational)
(if a whole number is not a perfect square, its square is irrational ex:)
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Rational numbers and irrational numbers form the set of Real numbers
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To which subsets of the real number system does each number belong?• 15