1. **State the problem:** We need to order the numbers 12 5/8, 12.62, $\sqrt{146}$, 12.39, and 12 3/4 from least to greatest. 2. **Convert mixed numbers to decimals:** - 12 5/8 = 12 + \frac{5}{8} = 12 + 0.625 = 12.625 - 12 3/4 = 12 + \frac{3}{4} = 12 + 0.75 = 12.75 3. **Approximate the square root:** - $\sqrt{146} \approx 12.083$ (since $12^2 = 144$ and $13^2 = 169$, $\sqrt{146}$ is slightly above 12) 4. **List all numbers as decimals:** - 12 5/8 = 12.625 - 12.62 (already decimal) - $\sqrt{146} \approx 12.083$ - 12.39 (already decimal) - 12 3/4 = 12.75 5. **Order from least to greatest:** - 12.083 ($\sqrt{146}$) - 12.39 - 12.62 - 12.625 (12 5/8) - 12.75 (12 3/4) Note that 12.62 < 12.625, so 12.62 comes before 12 5/8. 6. **Final order:** $$\sqrt{146}, 12.39, 12.62, 12 \frac{5}{8}, 12 \frac{3}{4}$$ This matches the first answer choice.