Lesson 4: Comparing and Ordering Real Numbers — Practice Questions

1. 1. Which of the following correctly compares the numbers $\sqrt{11}$ and $\frac{10}{3}$?

   • A. $\sqrt{11} < \frac{10}{3}$
   • B. $\sqrt{11} > \frac{10}{3}$
   • C. $\sqrt{11} = \frac{10}{3}$
   • D. The relationship cannot be determined

2. 2. Which list shows the numbers $-\sqrt{10}$, $-3.5$, $\frac{5}{2}$, and $\sqrt{2}$ in order from least to greatest?

   • A. $-3.5, -\sqrt{10}, \sqrt{2}, \frac{5}{2}$
   • B. $-\sqrt{10}, -3.5, \frac{5}{2}, \sqrt{2}$
   • C. $-3.5, -\sqrt{10}, \frac{5}{2}, \sqrt{2}$
   • D. $\frac{5}{2}, \sqrt{2}, -\sqrt{10}, -3.5$

3. 3. What is the greatest integer that is less than $\sqrt{40}$? Enter the integer in the blank: ___

4. 4. Which inequality correctly compares the numbers $-\pi$ and $-\frac{22}{7}$?

   • A. $-\pi > -\frac{22}{7}$
   • B. $-\pi < -\frac{22}{7}$
   • C. $-\pi = -\frac{22}{7}$
   • D. The numbers are opposites

5. 5. The number $\frac{13}{4}$ lies between which two consecutive integers? Enter the smaller of the two integers: ___

6. 6. Which statement correctly compares the numbers $\sqrt{10}$ and $\frac{16}{5}$?

   • A. $\sqrt{10} < \frac{16}{5}$
   • B. $\sqrt{10} > \frac{16}{5}$
   • C. $\sqrt{10} = \frac{16}{5}$
   • D. The relationship cannot be determined.

7. 7. Which list shows the numbers in order from least to greatest?

   • A. $-2.5, -\sqrt{5}, \frac{1}{4}, \sqrt{2}$
   • B. $-\sqrt{5}, -2.5, \frac{1}{4}, \sqrt{2}$
   • C. $-2.5, -\sqrt{5}, \sqrt{2}, \frac{1}{4}$
   • D. $\sqrt{2}, \frac{1}{4}, -\sqrt{5}, -2.5$

8. 8. On a number line, the irrational number $\sqrt{15}$ is located between the two consecutive integers ___ and 4.

9. 9. From the set of numbers {$\pi$, $\sqrt{8}$, $2.9$, $\frac{11}{4}$}, the greatest value is ___.