Lesson 12.1: Numbers, Numbers, and More Numbers! — Practice Questions

1. 1. The integer $-15$ can be written as a rational number in the form $\frac{p}{q}$. If the denominator $q$ is $1$, what is the value of the numerator $p$? ___

2. 2. Which of the following expressions does NOT represent a rational number?

   • A. $\frac{5}{8}$
   • B. $-9$
   • C. $\frac{12}{0}$
   • D. $\frac{-4}{3}$

3. 3. The mixed number $-3\frac{1}{4}$ is a rational number. When written as an improper fraction $\frac{p}{q}$, what is the value of the numerator $p$? ___

4. 4. According to the definition of rational numbers, which of the following statements is true?

   • A. All rational numbers are positive.
   • B. Only fractions are rational numbers.
   • C. An integer is not a rational number.
   • D. All integers are rational numbers.

5. 5. Write the rational number $5\frac{2}{7}$ as an improper fraction in the form $\frac{p}{q}$. What is the value of $p$? ___

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 ___.