\begin{tabular}{l} Convert \( 1^{\circ} 49^{\prime} 3^{\prime \prime} \) to a decimal number of degrees. \\ Do not round any intermediate computations. \\ Round your answer to the nearest thousandth. \\ \hline\( \square^{\circ} \)\end{tabular}

To convert \( 1^{\circ} 49^{\prime} 3^{\prime \prime} \) to a decimal number of degrees, we can follow these steps: 1. Convert the minutes and seconds to degrees. We know that: - 1 minute = \( \frac{1}{60} \) degrees - 1 second = \( \frac{1}{3600} \) degrees 2. Convert \( 49^{\prime} \): \[ 49^{\prime} = 49 \times \frac{1}{60} = \frac{49}{60} \text{ degrees} \] 3. Convert \( 3^{\prime \prime} \): \[ 3^{\prime \prime} = 3 \times \frac{1}{3600} = \frac{3}{3600} \text{ degrees} \] Now, we can combine these conversions: \[ \text{Total Decimal Degrees} = 1 + \frac{49}{60} + \frac{3}{3600} \] Now calculate each step: - Calculate \( \frac{49}{60} \): \[ \frac{49}{60} = 0.8166667 \text{ (approximately)} \] - Calculate \( \frac{3}{3600} \): \[ \frac{3}{3600} = 0.0008333 \text{ (approximately)} \] Putting it all together: \[ \text{Total Decimal Degrees} = 1 + 0.8166667 + 0.0008333 = 1.8175 \] Finally, round this to the nearest thousandth: \[ \boxed{1.818^{\circ}} \]