\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}

Question

UpStudy AI · Accepted Answer

To convert $$ 1^{\circ} 49^{\prime} 3^{\prime \prime} $$ to a decimal number of degrees, follow these steps:

1. **Understand the Conversion Factors:**
   - $$ 1^{\circ} = 1 $$ degree
   - $$ 1^{\prime} = \frac{1}{60} $$ degrees
   - $$ 1^{\prime \prime} = \frac{1}{3600} $$ degrees

2. **Apply the Conversion:**
   $$
   \text{Decimal Degrees} = 1^{\circ} + \frac{49^{\prime}}{60} + \frac{3^{\prime \prime}}{3600}
   $$
   
3. **Calculate Each Component:**
   $$
   \frac{49^{\prime}}{60} = \frac{49}{60} \approx 0.816666\ldots
   $$
   $$
   \frac{3^{\prime \prime}}{3600} = \frac{3}{3600} \approx 0.000833\ldots
   $$
   
4. **Sum the Components:**
   $$
   1 + 0.816666\ldots + 0.000833\ldots = 1.8175
   $$
   
5. **Round to the Nearest Thousandth:**
   $$
   1.8175 \text{ rounds to } 1.818 \text{ degrees}
   $$
   
**Final Answer:**
$$
1.818^{\circ}
$$
$$ 1.818^{\circ} $$

Convert to a decimal number of degrees.

Do not round any intermediate computations.

Round your answer to the nearest thousandth.

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Convert to a decimal number of degrees. Do not round any intermediate computations. Round your answer to the nearest thousandth.