Math behind converting from Decimal Degrees to Degrees:Minutes:Seconds
Courtesy of Dave Cochrun
Here is an example of the math involved in making a conversion from decimal degrees to degrees, minutes, seconds or DMS.  DMS is very similar to clock time hours, minutes, seconds.  Each hour (day) is divided into 60 minutes and each minute is divided into 60 seconds.  

We are going to convert Latitude 30.181360 and Longitude -85.781929 to Degrees : Minutes :Seconds

First lets tackle the Latitude of  30.181360 
  1. Keep the whole degrees (30) and put that in the D field. D = 30, M = ?, S=?
  2. Take everything to the right of the decimal point and the decimal point and multiply by 60 like this... 0.181360 x 60 = 10.8816 This is the decimal number of minutes.
  3. ;Keep the whole minutes (10) and put that in the M field. D = 30, M=10, S=?
  4. Take everything to the right of the decimal point and the decimal point and multiply by 60 like this... 0.8816 x 60 = 52.896 This is the decimal number of seconds. Put this number in the S field D = 30, M = 10, S = 52.896 Now keep the 52 for seconds. Since the decimal part of the seconds is larger than 0.50 you would round up the seconds to 53.
  5. So you enter 30:10:53 into the hand controller input field. The Gemini hand controller does not show Seconds on the Site page, but you can enter it in the input box on the entry page.
Now lets do the Longitude of -85.781929
  1. Keep the whole degrees (-85) and put that in the D field. D = -85, M = ?, S=?
  2. Take everything to the right of the decimal point and the decimal point and multiply by 60 like this... 0.781929 x 60 = 46.9157 This is the decimal number of minutes.
  3. Keep the whole minutes (46) and put that in the M field D = -85, M=46, S=?
  4. Take everything to the right of the decimal point and the decimal point and multiply by 60 like this... 0.9157 x 60 = 54.942This is the decimal number of seconds. Put this number in the S field. D = -85, M = 46, S = 54.942 Now keep the 54 for seconds. Since the decimal part of the seconds is larger than 0.50 you would round up the seconds to 55.
  5. So you enter -85:46:55 into the hand controller input field. The Gemini hand controller does not show Seconds on the Site page, but you can enter it in the input box on the entry page.