Lesson 1: Operations on Real Numbers — Practice Questions

1. 1. The number $\frac{31}{7}$ is a rational number. To which other set of numbers must it also belong?

   • A. Irrational numbers
   • B. Real numbers
   • C. Integers
   • D. Whole numbers

2. 2. Consider the numbers $-8$, $\frac{5}{2}$, and $-\sqrt{10}$. How many of these numbers are real numbers? ___

3. 3. Which of the following statements is false?

   • A. Every rational number is a real number.
   • B. The number $\sqrt{7}$ is a real number.
   • C. Every real number is an irrational number.
   • D. The number $-50$ is a real number.

4. 4. The number $-\sqrt{21}$ is an irrational number. Which statement correctly describes this number?

   • A. It is a real number.
   • B. It is not a real number.
   • C. It is both a rational and a real number.
   • D. It can be written as a simple fraction.

5. 5. True or False: Every real number is either a rational number or an irrational number.

   • A. True
   • B. False

6. 6. From the set $\{-8, 0, 1.95286\ldots, \frac{12}{5}, \sqrt{36}, 9\}$, identify the irrational number.

   • A. $1.95286\ldots$
   • B. $\frac{12}{5}$
   • C. $\sqrt{36}$
   • D. $-8$

7. 7. Which of the following numbers is an irrational number?

   • A. $\sqrt{81}$
   • B. $\frac{9}{4}$
   • C. $\sqrt{11}$
   • D. $5.75$

8. 8. The number $8.454454445...$ continues in this pattern without repeating. This number is an example of an ___ number.

9. 9. Which statement best describes why $\pi$ is considered an irrational number?

   • A. It is a ratio of two integers.
   • B. Its decimal form terminates.
   • C. Its decimal form is infinite and non-repeating.
   • D. It is a negative number.

10. 10. From the set $\{ \sqrt{100}, -4, \frac{3}{5}, \sqrt{5} \}$, the irrational number is ___.