Rational Numbers in Mathematics
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Questions and Answers

What is the definition of a rational number?

  • A number that can only be positive or negative.
  • A number that can be expressed in the form of $p/q$ where $q$ is not zero. (correct)
  • A number that cannot be expressed as a fraction.
  • A whole number that is an integer.

Which of the following is NOT a rational number?

  • $ rac{ ext{pi}}{2}$ (correct)
  • $ rac{7}{2}$
  • $4/3$
  • $0.75$

Which of the following statements about rational numbers is false?

  • A rational number must have a denominator of 1. (correct)
  • All integers are rational numbers.
  • A fraction with a non-zero denominator is a rational number.
  • Rational numbers can be represented as terminating or repeating decimals.

Which of the following fractions represents a rational number?

<p>$2/5$ (A), $3/3$ (C)</p> Signup and view all the answers

If $x$ is a rational number, which of the following must be true?

<p>$x$ can be expressed as $p/q$ where $q$ is a non-zero integer. (C)</p> Signup and view all the answers

Study Notes

Rational Numbers

  • Rational numbers are a subset of real numbers characterized by their representation in the form of ( p/q ), where ( p ) and ( q ) are integers and ( q \neq 0 ).
  • The denominator ( q ) must always be a non-zero value; fractions with zero denominators are undefined.
  • Common examples include fractions such as ( 1/2 ), ( 1/5 ), and ( 3/4 ).
  • Rational numbers can be expressed as terminating or repeating decimals, indicating they can be precisely represented on the number line.
  • All integers are considered rational numbers since they can be expressed as themselves over one (e.g., ( 5 ) can be written as ( 5/1 )).

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