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Gr 10 Math Ch 1: Rational and Irational Numbers
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Gr 10 Math Ch 1: Rational and Irational Numbers

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@GreatestTiger

Questions and Answers

What is the definition of a rational number?

  • A number that can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \) (correct)
  • A number that has a non-terminating, non-repeating decimal expansion
  • A number that can be written as a non-repeating, non-terminating decimal
  • A number that can be expressed as a simple fraction with a denominator of 0

    • What is an example of a rational number?

  • √2
  • π
  • 0.123456789
  • 0.5 (correct)

    • How can a terminating decimal be converted into a rational number?

  • By subtracting the decimal from an integer
  • By multiplying the decimal by a power of 10
  • By adding the decimal to an integer
  • By expressing it as the sum of fractions with denominators that are powers of 10 (correct)

    • What is the characteristic of an irrational number?

    <p>It has a non-terminating, non-repeating decimal expansion</p> Signup and view all the answers

    What happens when an irrational number is rounded off?

    <p>It becomes a rational number</p> Signup and view all the answers

    What is the result of converting a recurring decimal into a rational number?

    <p>A fraction with an integer numerator and denominator</p> Signup and view all the answers

    Which of the following is a characteristic of both rational and irrational numbers?

    <p>They are real numbers</p> Signup and view all the answers

    What can be said about the decimal expansion of a rational number?

    <p>It is either terminating or repeating</p> Signup and view all the answers

    Which of the following steps is used to convert a recurring decimal into a rational number?

    <p>Multiply the decimal by a power of 10 and then subtract the original equation</p> Signup and view all the answers

    What happens when an irrational number is expressed as a decimal?

    <p>It becomes a non-terminating and non-repeating decimal</p> Signup and view all the answers

    Why can't an irrational number be expressed as a simple fraction?

    <p>Because it has a non-terminating and non-repeating decimal expansion</p> Signup and view all the answers

    What is the result of converting a rational number into a decimal?

    <p>It becomes a terminating or repeating decimal</p> Signup and view all the answers

    What is the condition for a rational number to be expressed as a terminating decimal?

    <p>The denominator has no prime factors other than 2 or 5.</p> Signup and view all the answers

    Which of the following statements is true about rational and irrational numbers?

    <p>Rational and irrational numbers are mutually exclusive.</p> Signup and view all the answers

    What is the consequence of multiplying a recurring decimal by a power of 10?

    <p>The decimal expansion becomes terminating.</p> Signup and view all the answers

    Which of the following is a consequence of expressing an irrational number as a decimal?

    <p>The decimal expansion is non-repeating and non-terminating.</p> Signup and view all the answers

    What is the nature of the decimal expansion of a rational number?

    <p>Either terminating or repeating.</p> Signup and view all the answers

    What happens when an irrational number is approximated as a rational number?

    <p>The irrational number is approximated but remains distinct.</p> Signup and view all the answers

    Which of the following statements is true about a rational number?

    <p>Rational numbers can be expressed as a simple fraction with integer numerator and denominator.</p> Signup and view all the answers

    What is the result of subtracting the original equation from the new equation when converting a recurring decimal into a rational number?

    <p>The result is a linear equation with one variable.</p> Signup and view all the answers

    Why can't an irrational number be converted into a simple fraction?

    <p>Because it has a non-repeating and non-terminating decimal expansion.</p> Signup and view all the answers

    What happens when a rational number is expressed as a decimal?

    <p>The decimal expansion is always terminating or repeating.</p> Signup and view all the answers

    What is the condition for a rational number to be expressed as a terminating decimal?

    <p>The denominator must be a power of 2 or 5.</p> Signup and view all the answers

    Which of the following is a consequence of expressing a rational number as a decimal?

    <p>The rational number can be converted into a simple fraction.</p> Signup and view all the answers

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