Grade 8 Common Core Number System Quiz
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Questions and Answers

Which of the following statements is true about irrational numbers?

  • They are called rational numbers.
  • They have a decimal expansion that repeats eventually.
  • They have a decimal expansion that does not repeat or terminate. (correct)
  • They can be written as a fraction.

    • What does it mean for a decimal expansion to repeat eventually?

  • The decimal digits repeat exactly after a certain number of decimal places.
  • The decimal digits repeat in a predictable pattern. (correct)
  • The decimal digits repeat randomly.
  • The decimal digits do not repeat.

    • What is the relationship between rational and irrational numbers?

  • All rational numbers are also irrational numbers.
  • Rational and irrational numbers are mutually exclusive. (correct)
  • All irrational numbers are also rational numbers.
  • Rational and irrational numbers are the same thing.

    • What is the approximate value of $\pi^2$?

    <p>6.28</p> Signup and view all the answers

    How can rational approximations of irrational numbers be used to compare their sizes?

    <p>By finding rational numbers that are greater or smaller than the irrational numbers.</p> Signup and view all the answers

    Which of the following is an example of a negative exponent?

    <p>4^-2</p> Signup and view all the answers

    What does a negative exponent indicate?

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

    Which of the following is the reciprocal of 3^2?

    <p>1/9</p> Signup and view all the answers

    What is the value of 2^-3?

    <p>1/8</p> Signup and view all the answers

    If a number is raised to a negative exponent, what operation is involved?

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

    Study Notes

    Irrational Numbers

    • An irrational number is a real number that cannot be expressed as a finite decimal or fraction
    • Irrational numbers have infinite non-repeating decimal expansions

    Rational and Irrational Numbers

    • Rational numbers are a subset of real numbers that can be expressed as a finite decimal or fraction
    • Irrational numbers and rational numbers are mutually exclusive, but together they make up the set of real numbers

    Decimal Expansions

    • A decimal expansion that repeats eventually is a characteristic of rational numbers
    • Irrational numbers have unique, non-repeating decimal expansions that go on indefinitely

    Pi (π)

    • π is an irrational number, approximately equal to 3.14
    • The approximate value of π² is 9.86

    Exponents

    • A negative exponent indicates the reciprocal of the number
    • For example, 2⁻³ is equal to 1/2³, or 1/8
    • A negative exponent indicates that the operation involved is a reciprocal or "one over" the number
    • 3⁻² is an example of a negative exponent, indicating 1/3² or 1/9

    Comparing Irrational Numbers

    • Rational approximations of irrational numbers can be used to compare their sizes
    • By finding rational numbers close to the irrational numbers, comparisons can be made between them

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    Quiz Team

    Description

    Test your knowledge of Grade 8 Common Core Standards with this quiz! Explore the Number System and learn about rational and irrational numbers.

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