In Exercises 113-116, use the keys on your calculator or...

In Exercises $113-116,$ use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds $\left(D^{0} M^{\prime} S^{\prime \prime}\right)$ into decimal form, and vice versa. In Exercises $113-114,$ convert each angle to a decimal in degrees. Round your answer to two decimal places. $$ 30^{\circ} 15^{\prime} 10^{\prime \prime} $$

In Exercises $113-116,$ use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds $\left(D^{0} M^{\prime} S^{\prime \prime}\right)$ into decimal form, and vice versa.
In Exercises $113-114,$ convert each angle to a decimal in degrees. Round your answer to two decimal places.
$$
30^{\circ} 15^{\prime} 10^{\prime \prime}
$$

Key Concepts

Rounding

Rounding is the process of reducing the number of decimal places in a number to simplify the representation while maintaining a value that is close to the original number. In the context of angle conversions, rounding to a specified number of decimal places, such as two, ensures that the result is both precise and easily interpretable.

Conversion Between DMS and Decimal Degrees

The conversion between DMS and decimal degrees involves using the fact that one minute is one-sixtieth of a degree and one second is one-sixtieth of a minute. To convert a DMS value to decimal degrees, each segment (minutes and seconds) is divided by its respective factor (60 for minutes, 3600 for seconds) and added to the degree component.

Decimal Degrees

Decimal degrees are a way of writing angles using a decimal fraction instead of the traditional DMS format. This format simplifies calculations and is widely used in digital applications such as mapping and computer graphics.

Degrees, Minutes, and Seconds (DMS) Representation

The DMS format expresses an angle as a combination of degrees, minutes, and seconds, where one degree is subdivided into 60 minutes and one minute into 60 seconds. This representation is especially useful in fields like navigation and surveying where high precision is needed.

Angle Measurement

Angle measurement is the process of quantifying the amount of turn between two lines or rays. In different contexts, angles can be measured in several units, most commonly degrees, radians, or grads, with degrees being the most prevalent for everyday applications.

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