Mathematics Chapter 1.6 Summary: Rational and Irrational Numbers
6 Questions
2 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following statements is true about rational numbers?

  • Their decimal expansion is always non-terminating.
  • Rational numbers can never be negative.
  • All rational numbers are integers.
  • They can always be written in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q = 0$. (correct)

    • What is a key characteristic of irrational numbers?

  • They can always be expressed as fractions.
  • The sum of an irrational number and a rational number is always irrational.
  • Their decimal expansion is always non-repeating. (correct)
  • Irrational numbers are a subset of rational numbers.

    • Which of the following is true about the decimal expansion of rational numbers?

  • It can be either terminating or non-terminating recurring. (correct)
  • Rational numbers have unique decimal expansions.
  • The decimal expansion of a rational number is always an integer.
  • It is always non-recurring.

    • If $r$ is a rational number and $s$ is an irrational number, what can be said about $rs$?

    <p>$rs$ is always irrational.</p> Signup and view all the answers

    For positive real numbers $a$ and $b$, which of the following identities always holds?

    <p>$(a+b)(a-b) = a^2 - b^2$</p> Signup and view all the answers

    How can the denominator of $\frac{1}{a+b}$ be rationalized?

    <p>Multiply by $a-b$</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser