Convert the following angle to decimal degrees. \[ \alpha=74^{\circ} 51^{\prime} 49^{\prime \prime} \] $\alpha \approx$ (Round to 3 decimal places as needed)

Step 1 ：The given angle is in degrees, minutes, and seconds. To convert this 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 = 74, minutes = 51, seconds = 49

Step 5 ：Converting minutes to degrees: \(\frac{51}{60} = 0.85\) degrees

Step 6 ：Converting seconds to degrees: \(\frac{49}{3600} = 0.01361111111111111\) degrees

Step 7 ：Adding all the degrees together: \(74 + 0.85 + 0.01361111111111111 = 74.864\) degrees

Step 8 ：Final Answer: The decimal degree representation of the angle \(\alpha=74^\circ 51^\prime 49^\prime \prime\) is \(\boxed{74.864}\) degrees