Large transparent blue crystals of vanadyl pyrophosphate, (VO)(2)P(2)O(7), were grown from a phosphorus pentoxide flux, and the single-crystal X-ray structure of (VO)(2)P(2)O(7) was determined with high precision. On the basis of spin dimer analysis, we examined the spin exchange interactions of (VO)(2)P(2)O(7) and its precursor VO(HPO(4)).0.5H(2)O. Our analysis of (VO)(2)P(2)O(7) using two high-precision crystal structures shows unambiguously that the V3-V4 chain has a larger spin gap than does the V1-V2 chain and that the super-superexchange (V-O...O-V) interaction is stronger than the superexchange (V-O-V) interaction in the V3-V4 chain while the opposite is true in the V1-V2 chain. Our analysis of VO(HPO(4)).0.5H(2)O reveals that the superexchange interaction must dominate over the super-superexchange interaction, in disagreement with the conclusion from a powder neutron scattering study of VO(DPO(4)).0.5D(2)O.