Gr 10 Math Ch 1: Rational and Irational Numbers
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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
  • Ï€
  • 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 (A)</p> Signup and view all the answers

What happens when an irrational number is rounded off?

<p>It becomes a rational number (D)</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 (B)</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 (A)</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 (A)</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 (C)</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 (A)</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 (A)</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 (C)</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. (A)</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. (B)</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. (C)</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. (D)</p> Signup and view all the answers

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

<p>Either terminating or repeating. (D)</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. (B)</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. (B)</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. (A)</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. (B)</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. (D)</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. (A)</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. (C)</p> Signup and view all the answers

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