Question

Convert the angle 35°58'38" to decimal degrees and round to the nearest hundredth of a degree.

How would I do this?

Answer 1

There are 60' (arcminutes) in a degree and 60" (arcseconds) in a minute.
So there are 60*60= 3600" in a degree.

What use is this knowledge?
Well, you've got 38", so that is 38/3600 of 1 degree.
Also, you have 58', which is 58/60 of a degree.
All you have to do now, is use your calculator to add 35 + 58/60 + 38/3600.

Of course, you could cheat: many calculators have a button just for this kind of conversion, but that would be, well, cheating.

Answer 2

Where did you get 38/3600

Answer 3

1" = 1/60 of 1', which is 1/60 of 1 degree, so 1"is 1/60 of 1/60 of a degree.
1/60 of 1/60 is 1/3600.
you've got 38"so it is 38 times 1/3600 is 38/3600.