Convert decimal to degrees (modified from https://gist.github.com/laurynas/519740)

float.rb

class Float
  
  # Convert decimal to degrees, minutes, seconds sexagesimal 
  # (used for GPS coordinates)
  def to_sexagesimal type
    direction = nil
    
    if type == 'lat'
      direction = self.positive? ? 'N' : 'S'
    elsif type == 'long'
      direction = self.positive? ? 'W' : 'E'
    end

    degrees = abs.floor
    x       = (abs - degrees) * 60
    minutes = x.floor
    seconds = (((x - minutes) * 60) * 100).round.to_f / 100

    "#{degrees}°#{minutes}'#{seconds.trim}\" #{direction}"    
  end

  def positive?
    self >= 0
  end

  def trim 
    i, f = self.to_i, self.to_f
    i == f ? i : f
  end
  
end

x = -59.9939027777778

puts -3.12.to_sexagesimal 'long'
puts -3.109055556.to_sexagesimal 'lat'