Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"

Verified step by step guidance

1. Start with the given angle in degrees, minutes, and seconds: 47° 25' 11".
2. To convert this to decimal degrees, first convert the minutes to a fraction of a degree: \( \frac{25}{60} \).
3. Next, convert the seconds to a fraction of a degree: \( \frac{11}{3600} \).
4. Add these fractions to the whole degrees: \( 47 + \frac{25}{60} + \frac{11}{3600} \).
5. Calculate the sum to get the angle in decimal degrees, rounding to the nearest thousandth if necessary.

Key Concepts

Decimal Degrees

Decimal degrees are a way of expressing angles using a decimal format, where the whole number represents degrees and the decimal part represents a fraction of a degree. For example, 47.4197° is equivalent to 47° 25' 11''. This format is commonly used in various applications, including GPS and mapping, due to its simplicity in calculations.

Degrees, Minutes, Seconds (DMS)

Degrees, minutes, and seconds (DMS) is a traditional method of measuring angles, where one degree is divided into 60 minutes, and each minute is further divided into 60 seconds. This system is particularly useful in navigation and astronomy, allowing for precise angle measurements. For instance, 47° 25' 11'' indicates 47 degrees, 25 minutes, and 11 seconds.

Conversion Between DMS and Decimal Degrees

Converting between DMS and decimal degrees involves mathematical operations where the minutes and seconds are converted into a decimal format. To convert DMS to decimal degrees, the formula is: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600). Conversely, to convert decimal degrees to DMS, the whole number is taken as degrees, and the decimal part is multiplied by 60 to find minutes and further multiplied by 60 to find seconds.