Question Video: Understanding How to Convert an Angle Expressed in Degrees, Minutes and Seconds to Only Degrees Without Using a Calculator

Daniel is trying to convert 81° 47′ 35″ to degrees only without using a calculator. First, he converts the minutes to degrees by dividing 47 by 60, and then he converts the seconds to minutes by dividing 35 by 60. Finally, he adds all of the parts of the degree to get his answer. His answer is 82.3667°. Is his process correct? If you think his process is wrong, which of the following is correct? [A] He should divide 35 seconds by 60 times 60 (3,600) to convert it to degrees. So, his answer will be 81.793°. [B] He should add all of the degrees, minutes, and seconds. So, his answer will be 163°. [C] I think the process is correct.

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Video Transcript

Daniel is trying to convert 81 degrees, 47 minutes, 35 seconds to degrees only without using a calculator. First, he converts the minutes to degrees by dividing 47 by 60, and then he converts the seconds two minutes by dividing 35 by 60. Finally, he adds all of the parts of the degree to get his answer. His answer is 82.3667 degrees. Is his process correct? If you think his process is wrong, which of the following is correct? (A) He should divide 35 seconds by 60 times 60 or 3600 to convert it to degrees. So, his answer will be 81.793 degrees. Is it option (B) he should add all of the degrees, minutes, and seconds. So, his answer will be 163 degrees? Or is it option (C) I think the process is correct?

Let’s begin by looking at the angle we are given: 81 degrees, 47 minutes, and 35 seconds. We recall here our notation for minutes and seconds, one quotation mark and two quotation marks, respectively. We also recall that one degree is equal to 60 minutes. This means that to convert from minutes to degrees, we need to divide by 60. Dividing 47 by 60 is correct in order to convert from minutes to degrees. This is equal to 0.7833 and so on or 0.783 recurring.

We also recall that there are 60 seconds in one minute. This means that we can divide 35 by 60 to convert seconds to minutes. However, we want our answer in degrees only, whereas this would give an answer in minutes. 60 multiplied by 60 is 3600. This means that one degree is equal to 3600 seconds. In order to convert 35 seconds into degrees, we would need to divide 35 by 3600. This means that Daniel’s process is not correct. He should have divided 35 by 3600 instead of by 60 to convert the seconds into degrees. The answer of 82.3667 degrees is incorrect.

The second part of our question wants us to identify the correct process. We have already established that option (C) cannot be the correct answer. As we need to divide 35 by 3600, option (A) looks like it could be correct. 35 divided by 3600 is equal to 0.00972 and so on. In order to calculate 81 degrees, 47 minutes, and 35 seconds in degrees only, we need to add 0.7833, 0.00972, and 81. This gives us an answer of 81.793 and so on degrees. Option (A) is the correct process that Daniel should have followed. We know that option (B) cannot be correct, as he has not converted the minutes and seconds into degrees. 163 degrees is not the same as 81 degrees, 47 minutes, and 35 seconds.

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