Rational & Irrational Numbers Unit Test

Answer 1

Sure! Here's a unit test on rational and irrational numbers. You can use this for educational purposes to assess understanding of the concepts. The test is divided into multiple choice, true/false, and open-ended questions.

Rational & Irrational Numbers Unit Test

Part 1: Multiple Choice

1. Which of the following numbers is a rational number? a) √2
   b) 3/4
   c) π
   d) e

2. The number -5 is: a) Irrational
   b) Rational
   c) Neither

3. Which of the following is NOT a characteristic of rational numbers? a) They can be expressed as a fraction.
   b) They have decimal expansions that are either terminating or repeating.
   c) They can be expressed as a non-repeating decimal.
   d) They can be positive or negative.

4. The decimal representation of 1/7 is: a) Terminating
   b) Repeating
   c) Both
   d) Neither

5. Which of the following is an example of an irrational number? a) 0.333...
   b) √3
   c) 1.5
   d) -2

Part 2: True/False

6. Every integer is a rational number.
   True / False

7. The square root of every positive integer is an irrational number.
   True / False

8. π (pi) is a rational number.
   True / False

9. The sum of two irrational numbers is always irrational.
   True / False

10. The number 0 is a rational number.
    True / False

Part 3: Open-Ended Questions

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

12. Describe the difference between terminating and repeating decimals with examples.

13. Explain why the square root of a non-perfect square (like √5) is considered an irrational number.

14. Find three examples of irrational numbers. Show how you determined they are irrational.

15. If you add two rational numbers, what type of number will the result be? Explain your reasoning.

Answer Key

Part 1: Multiple Choice

1. b) 3/4
2. b) Rational
3. c) They can be expressed as a non-repeating decimal.
4. b) Repeating
5. b) √3

Part 2: True/False

6. True
7. False (only perfect squares yield a rational result)
8. False
9. False (there are cases where the sum is rational, for example, √2 + (−√2) = 0)
10. True

Part 3: Open-Ended Questions

(Answers will vary based on student responses; assess based on clarity, correctness, and understanding of the concepts.)

Feel free to customize this test as needed!