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. 119° 08' 03"

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Step 1: Understand the problem. We need to convert the angle given in degrees, minutes, and seconds (DMS) format, 119° 08' 03", into decimal degrees.

Step 2: Recall the conversion formula. To convert from DMS to decimal degrees, use the formula: \( ext{Decimal Degrees} = ext{Degrees} + \frac{ ext{Minutes}}{60} + \frac{ ext{Seconds}}{3600} \).

Step 3: Substitute the given values into the formula. Here, Degrees = 119, Minutes = 8, and Seconds = 3.

Step 4: Calculate each component: \( \frac{8}{60} \) for minutes and \( \frac{3}{3600} \) for seconds, then add these to the degrees.

Step 5: Sum the values to get the final result in decimal degrees, rounding to the nearest thousandth if necessary.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, 119.1342 degrees indicates 119 degrees and a fraction of a degree. 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 expressing angles, where one degree is divided into 60 minutes, and one minute is divided into 60 seconds. For instance, 119° 08' 03'' represents 119 degrees, 8 minutes, and 3 seconds. This format is often used in navigation and surveying, providing a more precise representation of angles.

Conversion Between DMS and Decimal Degrees

Converting between DMS and decimal degrees involves mathematical operations where the minutes and seconds are converted into decimal form. 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 seconds. This conversion is essential for accurate calculations in trigonometry and navigation.

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