The source is one 8-inch round pan and the target is one 9-inch round pan. Counts match, units match, and both area formulas contain the same π ÷ 4 factor.
Write both symbolic areas
The 8-inch area is π × 8² ÷ 4 = 16π square inches. The 9-inch area is π × 9² ÷ 4 = 20.25π square inches. PanRatio may display their decimal areas with ≈ because π is irrational, but it retains the symbolic coefficients for the ratio.
Cancel pi before division
Target divided by source is 20.25π ÷ 16π. Pi cancels exactly, leaving 20.25 ÷ 16 = 81 ÷ 64 = 1.265625. The target pan has exactly 26.5625 percent more ideal base area than the source pan.
Scale 250 units only at the end
Multiply 250 by the exact fraction 81/64 to get 316.40625. Displaying four decimal places gives ≈316.4063; the approximation marker belongs to the displayed quantity, not to the exact pan ratio. Decide how to round a real ingredient according to that ingredient and recipe.