Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. 274° 18' 59"

Verified step by step guidance

1. Identify the components of the angle: degrees (°), minutes ('), and seconds ("). Here, the angle is 274° 18' 59".
2. Recall the conversion relationships: 1 minute = \(\frac{1}{60}\) degrees and 1 second = \(\frac{1}{3600}\) degrees.
3. Convert the minutes to decimal degrees by dividing the minutes by 60: \( 18' = \frac{18}{60} \) degrees.
4. Convert the seconds to decimal degrees by dividing the seconds by 3600: \( 59" = \frac{59}{3600} \) degrees.
5. Add the degrees, the converted minutes, and the converted seconds together to get the total angle in decimal degrees: \( 274 + \frac{18}{60} + \frac{59}{3600} \).

Key Concepts

Degrees, Minutes, and Seconds (DMS) Notation

Angles can be expressed in degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. This notation is commonly used in navigation and surveying to represent precise angle measurements.

Conversion from DMS to Decimal Degrees

To convert an angle from degrees, minutes, and seconds to decimal degrees, keep the degrees as is, convert minutes by dividing by 60, and convert seconds by dividing by 3600. Summing these values gives the angle in decimal degrees.

Rounding Decimal Values

After converting to decimal degrees, rounding to a specified precision, such as the nearest thousandth, ensures clarity and usability. This involves identifying the digit in the thousandths place and adjusting based on the following digit.