Convert the given angle to decimal degrees. Round to 4 decimal places.
\[
57^{\circ} 30^{\prime} 32^{\prime \prime} \approx
\]

Step 1 ：The given angle is in degrees, minutes, and seconds. To convert it to decimal degrees, we need to convert the minutes and seconds to degrees.

Step 2 ：1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds. Therefore, 1 degree is equal to 3600 seconds.

Step 3 ：So, to convert minutes to degrees, we divide the number of minutes by 60. To convert seconds to degrees, we divide the number of seconds by 3600.

Step 4 ：Given degrees = 57, minutes = 30, seconds = 32

Step 5 ：Converting minutes to degrees: \(\frac{30}{60} = 0.5\) degrees

Step 6 ：Converting seconds to degrees: \(\frac{32}{3600} = 0.008888888888888889\) degrees

Step 7 ：Adding all the degrees together: \(57 + 0.5 + 0.008888888888888889 = 57.5089\) degrees

Step 8 ：Final Answer: \(57^\circ 30^\prime 32^\prime \prime \approx \boxed{57.5089^\circ}\)