Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. 102.3771°

Verified step by step guidance

1. Identify the given angle in decimal degrees: \(102.3771^\circ\).
2. Separate the whole number part from the decimal part. The whole number part is the degrees: \(102^\circ\).
3. Convert the decimal part (0.3771) to minutes by multiplying by 60: \(0.3771 \times 60\).
4. Separate the whole number part of the minutes from the decimal part. The whole number is the minutes.
5. Convert the remaining decimal part of the minutes to seconds by multiplying by 60: (decimal part of minutes) \(\times 60\). Round to the nearest second if necessary.

Key Concepts

Decimal Degrees to Degrees, Minutes, and Seconds Conversion

This concept involves converting an angle expressed in decimal degrees into degrees, minutes, and seconds (D° M' S"). Degrees remain the integer part, minutes are obtained by multiplying the decimal remainder by 60, and seconds come from multiplying the new decimal remainder by 60 again.

Rounding to the Nearest Second

After calculating seconds in the conversion process, it is important to round the value to the nearest whole number to provide a precise and standardized angle measurement. This ensures clarity and consistency in reporting angles.

Understanding Angle Measurement Units

Degrees, minutes, and seconds are units used to measure angles, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This hierarchical structure allows for precise representation of angles smaller than one degree.