sloppycanada
  • sloppycanada
Write 15 degrees 26' 29" using decimal degrees. Round your answer to the nearest thousandth. I don't want someone to do this for me, please explain it to me.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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prizzyjade
  • prizzyjade
that is something you need to use a calculator
prizzyjade
  • prizzyjade
scientific calculator to be exact
sloppycanada
  • sloppycanada
@jim_thompson5910 When you get the chance...

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jim_thompson5910
  • jim_thompson5910
the `26'` means `26 minutes` or `26 arcminutes` the `29" ` means `29 seconds` or `29 arcseconds`
jim_thompson5910
  • jim_thompson5910
Rules: 1 degree = 60 arcminutes 1 arcminute = 60 arcseconds
jim_thompson5910
  • jim_thompson5910
sound familiar?
sloppycanada
  • sloppycanada
Yes.
jim_thompson5910
  • jim_thompson5910
using those rules, we can write `26 arcminutes` as `(26/60) degrees` 60 arcminutes will give you a full degree. So 26 arcminutes is going to be a fraction (smaller than 1) of a degree
jim_thompson5910
  • jim_thompson5910
1 degree = 60 arcminutes 1 arcminute = 60 arcseconds means 1 degree = 60*60 = 3600 arc seconds so `29 arcseconds = (29/3600) degrees`
sloppycanada
  • sloppycanada
Do I divide?
sloppycanada
  • sloppycanada
That would be .008
jim_thompson5910
  • jim_thompson5910
so, 15 degrees 26' 29" = (15 degrees) + (26/60 degrees) + (29/3600 degrees) 15 degrees 26' 29" = (15 + 26/60 + 29/3600) degrees 15 degrees 26' 29" = ??? degrees
sloppycanada
  • sloppycanada
15.441
jim_thompson5910
  • jim_thompson5910
yeah I'm getting 15.4413888888889
sloppycanada
  • sloppycanada
If I were to round that to the nearest thousandth, it's be 15.440
jim_thompson5910
  • jim_thompson5910
15.441 actually
sloppycanada
  • sloppycanada
Alright, the next thing asks me to change the 29 to 9. so it'd be 15 degrees 26' and 9"
sloppycanada
  • sloppycanada
Would that just be 15.436?
jim_thompson5910
  • jim_thompson5910
looks good 15 + 26/60 + 9/3600 = 15.4358333333333 ---> 15.436
sloppycanada
  • sloppycanada
45 degrees 9' 30"
sloppycanada
  • sloppycanada
45 + 9/60 + 30/3600 = 45.158
jim_thompson5910
  • jim_thompson5910
looks good \[\color{red}{45} \text{ degrees}, \color{blue}{9} \text{ minutes}, \color{green}{30} \text{ seconds} = (\color{red}{45} + \color{blue}{9}/60 + \color{green}{30}/3600) \text{degrees}\]

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