Algebra II Assignment 2: Real Numbers
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Questions and Answers

What is a rational number?

  • A nonterminating, nonrepeating decimal
  • A terminating or repeating decimal (correct)
  • A number that can be expressed as a quotient of two integers (correct)
  • A number that cannot be expressed as a quotient of two integers

    • What is an irrational number?

  • A repeating decimal
  • A number that cannot be expressed as a quotient of two integers (correct)
  • A terminating decimal
  • A number that can be expressed as a quotient of two integers

    • Is 1384 a rational number?

    Yes

    Is π a rational number?

    <p>No</p> Signup and view all the answers

    -0.28764... is what type of number?

    <p>Irrational</p> Signup and view all the answers

    Is 0 a rational number?

    <p>Yes</p> Signup and view all the answers

    -19.78 is what type of number?

    <p>Rational</p> Signup and view all the answers

    -√3/5 + 10.8 is what type of number?

    <p>Irrational</p> Signup and view all the answers

    -7.832198653... is what type of number?

    <p>Irrational</p> Signup and view all the answers

    -0.8662866239... is what type of number?

    <p>Irrational</p> Signup and view all the answers

    In $3√13$, what is the term called 13?

    <p>Radicand</p> Signup and view all the answers

    In $3√13$, what is the term called 3?

    <p>Index</p> Signup and view all the answers

    What is the expression $3√13$ called?

    <p>Radical</p> Signup and view all the answers

    0.225 equals 9/40.

    <p>True</p> Signup and view all the answers

    -0.6 equals -4/7.

    <p>False</p> Signup and view all the answers

    0.8 equals 8/10.

    <p>False</p> Signup and view all the answers

    -3.143 equals -3140/999.

    <p>True</p> Signup and view all the answers

    Study Notes

    Rational and Irrational Numbers

    • Rational Number: Can be expressed as a quotient of two integers; examples include terminating or repeating decimals.
    • Irrational Number: Cannot be expressed as a quotient of two integers; characterized by nonterminating, nonrepeating decimals.

    Examples of Rational Numbers

    • 1,384: Classified as a rational number.
    • 0: Considered a rational number since it can be expressed as 0/1.
    • -19.78: Also a rational number, expressible as -1978/100.

    Examples of Irrational Numbers

    • π (pi): A well-known irrational number not expressible as a simple fraction.
    • -0.28764...: An example of an irrational number with a nonterminating decimal.
    • -√3/5 + 10.8: Results in an irrational number.
    • -7.832198653... and -0.8662866239...: Both are classified as irrational due to their nonrepeating, nonterminating nature.

    Radicals and Their Components

    • In the expression ³√13:
      • Radicand: The number inside the radical, here it is 13.
      • Index: The number that indicates the root being taken, here it is 3.
      • Radical: The entire expression (³√13) is known as a radical.

    True or False Statements About Rational Numbers

    • True: 0.225 equals 9/40, confirming its rationality.
    • False: -0.6 equals -4/7; this statement is incorrect.
    • False: 0.8 is not equal to 8/10; this statement is false.
    • True: -3.143 equals -3140/999, verifying its classification as a rational number.

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    Test your knowledge of rational and irrational numbers with this flashcard quiz. You'll learn definitions and identify examples of each type of number. Great for preparing for Algebra II assessments!

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