Convert decimal degrees to degrees, minutes, seconds, and convert...

Question

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.                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                                                                                 
                                                                275.1005°

Accepted Answer

Hello, everyone. We are asked to convert the following angle to degrees. Minutes and seconds. We will round our answer to the nearest second. When necessary, we are given 178.5067 degrees. Our answer choices are a degrees. 51 minutes. Seven seconds. B 178 degrees, seven minutes, 51 seconds. C 178 degrees. 30 minutes, 24 seconds. D 178 degrees, 24 minutes, 30 seconds. First, recall that one degree is equal to 60 minutes. And then we also need to recall that one minute is comprised of 60 seconds. This will help us. So looking at what we're given 178.5067 degrees. So in the end, we're gonna have 178 degrees, but we gotta take that decimal piece and make it into minutes and seconds. So I'm gonna start with 0.5067 degrees. And if there are 60 minutes in one degree, I'm gonna multiply this decimal by 60 minutes. So I have 0.5067 degrees multiplied by 60 minutes per degree. And that will give us 30. minutes. So we're gonna take the 30 part of that and put it over here as part of our answer. So that's our gonna be our, our minutes, 30 minutes and now we'll take the decimal portion from our minutes. So 0.402 minutes and we're gonna multiply it by 60 seconds per minute, which when we do that, those multiply together to 24. seconds, we are told to run to the nearest second. So we will treat this as 24 seconds. So in the end, we have 178 degrees, 30 minutes, 24 seconds, which is answer choice C have a nice day.

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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. 275.1005°