### 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.