$55.27^{\circ}$ is the same as $55^{\circ}$ $\qquad$ $12^{\prime \prime}$?
Answer (1)
Convert the decimal part of the degree to minutes by multiplying by 60: 0.27 × 60 = 16.2 .
Take the whole number part as minutes (16) and convert the remaining decimal part to seconds.
Convert the decimal part of the minutes to seconds by multiplying by 60: 0.2 × 60 = 12 .
Express the final answer in degrees, minutes, and seconds: 5 5 ∘ 1 6 ′ 1 2 ′′ .
Explanation
Problem Analysis We are given an angle in degrees as 55.2 7 ∘ and we want to express it in degrees, minutes, and seconds. We know that 55.2 7 ∘ is the same as 5 5 ∘ plus some minutes and seconds. Our goal is to convert the decimal part, 0.2 7 ∘ , into minutes and seconds.
Convert to Minutes To convert the decimal part of the degree measure to minutes, we multiply by 60, since there are 60 minutes in a degree: 0.2 7 ∘ × 60 degree minutes = 16.2 minutes So, we have 16 full minutes and a decimal part of 0.2 minutes.
Convert to Seconds Now, we convert the decimal part of the minutes to seconds. We multiply by 60 again, since there are 60 seconds in a minute: 0.2 minutes × 60 minute seconds = 12 seconds So, we have 12 seconds.
Final Answer Therefore, 55.2 7 ∘ is equal to 5 5 ∘ 16 minutes and 12 seconds, which we write as 5 5 ∘ 1 6 ′ 1 2 ′′ .
Examples
Understanding angles in degrees, minutes, and seconds is crucial in navigation and astronomy. For example, when using a sextant to measure the angle to a star, navigators need to convert decimal degrees into minutes and seconds to pinpoint their location accurately. Similarly, astronomers use this system to precisely define the positions of celestial objects in the sky, allowing for detailed mapping and study of the universe.
