Question

Write the measure 29° 6' 6" as decimal to the nearest thousandth.

Answer 1

This angle is "29 degrees 6 minutes 6 seconds".

-- There are 60 minutes in 1 degree. 
     So 1 minute = 1/60 degree.

-- There are 60 seconds in 1 minute. 
      So 1 second = 1/60 minute = 1/3600 degree.

  29  6'  6"  =  (29)° + (6/60)° + (6/3600)°

                   =  (29)° + (0.1)° + (0.001666...)°

                   =        29.101666...°

Rounded to the nearest thousandth of a degree:  29.102°