Changing degrees to a decimal

Question

How do you change 78° 15'  50" to a number of degrees to the nearest thousandth?

Answer 1

degrees are equivalent to hours which are also divided into minutes and seconds.

 

we use the ratios 60 minutes in 1 hour (also 1 degree) and 60 seconds in 1 minute.

 

15' is 15 minutes which is 15/60 = 1/4 degree (similar to 1/4 hour) = .25

 

50" is 50 seconds which is 50/60 minutes or 50/3600 degrees = .014

 

So adding it together we have in degrees   78 + .25 + .014 = 78.264 degrees

Answer 2

There are 60 seconds in 1 minute and 60 minutes in 1 degree.

 

So, 78º 15' 50" = 78 + 15/60 + 50/3600 = 78.264º to the nearest thousandth.