Question

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.

Answer 1

that is something you need to use a calculator

Answer 2

scientific calculator to be exact

Answer 3

@jim_thompson5910 When you get the chance...

Answer 4

the `26'` means `26 minutes` or `26 arcminutes`

the `29" ` means `29 seconds` or `29 arcseconds`

Answer 5

Rules:

1 degree = 60 arcminutes
1 arcminute = 60 arcseconds

Answer 6

sound familiar?

Answer 7

Yes.

Answer 8

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

Answer 9

1 degree = 60 arcminutes
1 arcminute = 60 arcseconds

means

1 degree = 60*60 = 3600 arc seconds

so `29 arcseconds = (29/3600) degrees`

Answer 10

Do I divide?

Answer 11

That would be .008

Answer 12

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

Answer 13

15.441

Answer 14

yeah I'm getting 15.4413888888889

Answer 15

If I were to round that to the nearest thousandth, it's be 15.440

Answer 16

15.441 actually

Answer 17

Alright, the next thing asks me to change the 29 to 9. so it'd be 15 degrees 26' and 9"

Answer 18

Would that just be 15.436?

Answer 19

looks good

15 + 26/60 + 9/3600 = 15.4358333333333 ---> 15.436

Answer 20

45 degrees 9' 30"

Answer 21

45 + 9/60 + 30/3600 = 45.158

Answer 22

looks good
\[\color{red}{45} \text{ degrees}, \color{blue}{9} \text{ minutes}, \color{green}{30} \text{ seconds} = (\color{red}{45} + \color{blue}{9}/60 + \color{green}{30}/3600) \text{degrees}\]