9-37: Order these real numbers from least to greatest. A number line may be helpful. \( -1 \frac{3}{9} ; 0.25 ; \sqrt[3]{27} ; \pi ;-0 . \overline{6} ;-\sqrt{16} \)

To order the given real numbers from least to greatest, let's first convert them into decimal or simplified forms: 1. \( -1 \frac{3}{9} \) can be simplified: \[ -1 \frac{3}{9} = -1 \frac{1}{3} = -1.3333\ldots \text{ (or } -1.33\text{)} \] 2. \( 0.25 \) is already in decimal form. 3. \( \sqrt[3]{27} \) is: \[ \sqrt[3]{27} = 3 \] 4. \( \pi \) is approximately: \[ \pi \approx 3.14159 \] 5. \( -0.\overline{6} \) is a repeating decimal: \[ -0.\overline{6} = -\frac{2}{3} \approx -0.6666\ldots \] 6. \( -\sqrt{16} \) is: \[ -\sqrt{16} = -4 \] Now we have the following values: - \( -1.3333\ldots \) (or \( -1 \frac{1}{3} \)) - \( 0.25 \) - \( 3 \) - \( \pi \approx 3.14159 \) - \( -0.6666\ldots \) (or \( -\frac{2}{3} \)) - \( -4 \) Next, let's list these values in order from least to greatest: 1. \( -4 \) 2. \( -1.3333\ldots \) (or \( -1 \frac{1}{3} \)) 3. \( -0.6666\ldots \) (or \( -\frac{2}{3} \)) 4. \( 0.25 \) 5. \( 3 \) 6. \( \pi \) Thus, the ordered list from least to greatest is: \[ -4, -1 \frac{1}{3}, -0.\overline{6}, 0.25, 3, \pi \]