Order the numbers from least to greatest. and sleth your numbcr lines \( \begin{array}{l}\text { 13. } \sqrt{99}, \pi^{2}, 9 . \overline{8} \frac{7}{2}, 9 . \overline{8} \sqrt{99} \\ \text { ESSENTIALQUESTION } \\ \text { 14. } \sqrt{\frac{1}{25}}, \frac{1}{4}, 0 . \overline{2} \sqrt{\frac{1}{2}}, 0 . \overline{2}, \frac{1}{4} \\ \text { 15. How are real numbers used to describe real-world situations? }\end{array} \)

Certainly! Let's tackle each of your questions step-by-step. --- ### **Problem 13** **Order the numbers from least to greatest:** \[ \sqrt{99},\ \pi^{2},\ 9.\overline{8} \times \frac{7}{2},\ 9.\overline{8} \times \sqrt{99} \] **Step 1: Calculate or Approximate Each Value** 1. **\(\sqrt{99}\)** \[ \sqrt{99} \approx 9.9499 \] 2. **\(\pi^{2}\)** \[ \pi^{2} \approx 3.1416^{2} \approx 9.8696 \] 3. **\(9.\overline{8} \times \frac{7}{2}\)** \[ 9.\overline{8} = 9.8888\ldots \\ 9.8888 \times 3.5 = 34.6111\ldots \] 4. **\(9.\overline{8} \times \sqrt{99}\)** \[ 9.8888 \times 9.9499 \approx 98.4375 \] **Step 2: Order the Numbers** Based on the approximations: \[ \pi^{2} \approx 9.8696 < \sqrt{99} \approx 9.9499 < 34.6111 < 98.4375 \] **Final Order (Least to Greatest):** \[ \pi^{2},\ \sqrt{99},\ 9.\overline{8} \times \frac{7}{2},\ 9.\overline{8} \times \sqrt{99} \] --- ### **Problem 14** **Order the numbers from least to greatest:** \[ \sqrt{\frac{1}{25}},\ \frac{1}{4},\ 0.\overline{2} \times \sqrt{\frac{1}{2}},\ 0.\overline{2},\ \frac{1}{4} \] **Step 1: Calculate or Approximate Each Value** 1. **\(\sqrt{\frac{1}{25}}\)** \[ \sqrt{\frac{1}{25}} = \frac{1}{5} = 0.2 \] 2. **\(\frac{1}{4}\)** \[ \frac{1}{4} = 0.25 \] 3. **\(0.\overline{2} \times \sqrt{\frac{1}{2}}\)** \[ 0.\overline{2} = 0.2222\ldots \\ \sqrt{\frac{1}{2}} \approx 0.7071 \\ 0.2222 \times 0.7071 \approx 0.1571 \] 4. **\(0.\overline{2}\)** \[ 0.\overline{2} = 0.2222\ldots \] 5. **\(\frac{1}{4}\)** \[ \frac{1}{4} = 0.25 \] **Step 2: Order the Numbers** Based on the approximations: \[ 0.1571 < 0.2 < 0.2222\ldots < 0.25 = 0.25 \] **Final Order (Least to Greatest):** \[ 0.\overline{2} \times \sqrt{\frac{1}{2}},\ \sqrt{\frac{1}{25}},\ 0.\overline{2},\ \frac{1}{4},\ \frac{1}{4} \] --- ### **Problem 15** **How are real numbers used to describe real-world situations?** Real numbers are fundamental in representing and modeling various aspects of the real world. Here's how they are utilized: 1. **Measurement**: Quantities such as length, mass, time, temperature, and volume are expressed using real numbers. For example, a room might be 12.5 meters long, and water might be heated to 75.3°C. 2. **Finance**: Transactions involve real numbers in the form of prices, interest rates, budgets, and expenses. For instance, purchasing an item for \$19.99 or calculating interest at a rate of 3.5%. 3. **Engineering and Science**: Precise calculations in engineering designs, physics experiments, and chemical compositions rely on real numbers to ensure accuracy and functionality. 4. **Technology**: Digital systems use real numbers to process and represent data, such as in graphics rendering, signal processing, and statistical analyses. 5. **Everyday Activities**: Real numbers help in everyday tasks like cooking (measuring ingredients), shopping (calculating discounts), and scheduling (keeping track of time). 6. **Statistics and Data Analysis**: Real numbers are essential for analyzing data, understanding trends, and making informed decisions based on numerical information. 7. **Navigation and Mapping**: Coordinates on maps are represented using real numbers to specify precise locations on Earth. In essence, real numbers provide a versatile and precise language that allows us to quantify, analyze, and navigate the myriad phenomena in our daily lives and the broader universe. --- If you need further clarification or assistance with any of these problems, feel free to ask!