rational numbers and irrational numbers unit test

1 answer

Sure! Here’s a unit test on rational and irrational numbers. This test includes a variety of question types, including multiple choice, short answer, and problems that require explanations.


Rational and Irrational Numbers Unit Test

Name: _________________________
Date: _________________________


Part 1: Multiple Choice (1 point each)

  1. Which of the following is a rational number? a) \( \sqrt{2} \)
    b) \( \frac{1}{3} \)
    c) \( \pi \)
    d) \( e \)

  2. Which number is irrational? a) -1
    b) 0
    c) \( \sqrt{9} \)
    d) \( \sqrt{5} \)

  3. The sum of two rational numbers is: a) Always rational
    b) Always irrational
    c) Sometimes rational, sometimes irrational
    d) None of the above

  4. Which of the following intervals contains only irrational numbers? a) \( (0, 1) \)
    b) \( (1, 2) \)
    c) \( (\sqrt{2}, \sqrt{3}) \)
    d) \( (3, \sqrt{5}) \)


Part 2: Short Answer (2 points each)

  1. Provide an example of a rational number and explain why it is rational.

    Answer: _________________________________________________________

  2. Provide an example of an irrational number and explain why it is irrational.

    Answer: _________________________________________________________

  3. Explain the difference between rational and irrational numbers.

    Answer: _________________________________________________________


Part 3: Problems (3 points each)

  1. Determine whether the following numbers are rational or irrational:
    a) \( -\frac{7}{2} \)
    b) \( 0.3333... \) (repeating)
    c) \( \frac{22}{7} \)
    d) \( \sqrt{16} \)
    e) \( \sqrt{3} \)

    Answers:
    a) _______________
    b) _______________
    c) _______________
    d) _______________
    e) _______________

  2. If a rational number is expressed as a decimal, can it be a non-terminating decimal? Explain your answer.

    Answer: _________________________________________________________

  3. If you add an irrational number to a rational number, what type of number do you get? Justify your answer with an example.

    Answer: _________________________________________________________


Part 4: True or False (1 point each)

  1. Every whole number is a rational number. (True/False)
  2. The number \( \frac{0}{10} \) is irrational. (True/False)
  3. The product of two irrational numbers is always irrational. (True/False)

Scoring Guide:

  • Part 1: 4 points total
  • Part 2: 6 points total
  • Part 3: 15 points total
  • Part 4: 3 points total

Total Points: 28


Instructions for Grading:

  • Correct answers in Part 1 and Part 4 receive full points; partial credit may be given for explanations if needed.
  • For Parts 2 and 3, evaluate based on the completeness and correctness of the explanations and examples provided.

Feel free to modify any part of the test to better suit your needs!