Context. Dust grains coagulate in protoplanetary disks to form fluffy aggregates. Theoretical and experimental studies have shown that the internal density of dust aggregates is expected to be as small as \(10^{-4} {\rm ~g~cm^{-3}}\). Disk observations, on the other hand, are interpreted as the emission from compact grains. The emission may come from fluffy aggregates. However, optical properties of such fluffy aggregates have been poorly understood. Aims. We aim to reveal the mass opacity of fluffy aggregates at from infrared to millimeter wavelengths with the filling factor ranging from 1 down to \(10^{-4}\). Methods. We use Mie calculations with an effective medium theory. The monomers are assumed to be 0.1 micron-sized grains, which is much shorter than the wavelengths which we focus on. Results. We find that the absorption mass opacity of fluffy aggregates are well characterized by the product \(a\times f\), where \(a\) is the dust radius and \(f\) is the filling factor, except for the interference structure. The scattering mass opacity is also well characterized by a f at short wavelengths while it is higher in more fluffy aggregates at long wavelengths. We also derive the analytic formula of the mass opacity and find that it well reproduces the Mie calculations. We also calculate the expected difference of the emission between compact and fluffy aggregates in protoplanetary disks with a simple dust growth and drift model. We find that the compact and fluffy aggregates can be distinguished by the radial distribution of the opacity index beta. The previous observation of the radial distribution of beta is consistent with the fluffy case, but more observations are required to distinguish fluffy or compact. In addition, we find that the scattered light would be another clue to distinguish the compact and fluffy aggregates.