The correct formula to solve the coefficient q for grid to geographic conversion is:

• A. q = 0.0001(E')
• B. q = 0.000001(E)
• C. q = 0.00001(E')
• D. q = 0.000001(E')

Answer: (D)

The main idea is that grid-to-geographic conversions use a tiny linear factor to turn grid distance into an angular change on the earth. The coefficient q serves to convert a distance in the corrected Easting (E′) into a corresponding change in geographic longitude, expressed in degrees. Because geographic angles are small when you translate meters on the grid, the factor needs to be very small—on the order of parts per million per meter—so that a typical grid step maps to a sensible fraction of a degree. Using the corrected Easting E′ is essential: it accounts for the projection’s local offsets and distortions, making the relationship effectively linear around the working point. The chosen value of 0.000001 degrees per unit of E′ yields realistic, stable corrections over the grid, whereas using a larger factor or applying the factor to the uncorrected Easting would misrepresent the distortion and produce too large adjustments.