Question

Convert the angle measures given in DMS form to decimal degrees with three decimal places. $$150^{\circ} 40^{\prime} 20^{\prime \prime}$$

   Convert the angle measures given in DMS form to decimal degrees with three decimal places.
$$150^{\circ} 40^{\prime} 20^{\prime \prime}$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 5, Problem 74

Instant Answer

Solved by Expert Gianna Calciano

06/30/2020

Step 1

We do this by dividing the minutes by 60 and the seconds by 3600. This is because there are 60 minutes in a degree and 3600 seconds in a degree. So, we have: $$40^{\prime} = \frac{40}{60} = 0.666... \text{ degrees}$$ $$20^{\prime \prime} = \frac{20}{3600} = Show more…

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Convert the angle measures given in DMS form to decimal degrees with three decimal places. $$150^{\circ} 40^{\prime} 20^{\prime \prime}$$

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Key Concepts

Rounding and Precision

Rounding is the process of adjusting a numerical value to a specified degree of precision. In many applications, including angle conversions, it is common to round the final result to a fixed number of decimal places (such as three) to ensure consistency and manageability in subsequent computations.

DMS Notation

DMS stands for Degrees, Minutes, and Seconds, a way to represent angular measurements where one degree is divided into 60 minutes and one minute into 60 seconds. This notation is widely used in fields like navigation, surveying, and astronomy to provide a detailed description of angular positions.

Decimal Degrees Conversion

Converting DMS to decimal degrees involves expressing the entire angle as a single number in degrees. This is done by adding the degrees to the minutes divided by 60 and the seconds divided by 3600. This conversion simplifies calculations in computer algorithms and many mathematical applications.

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