Notes:

1. This definition implies the exact relation ${\Delta\nu_{\rm{Cs}}} = {{9\:192\:631\:770}}\ {{\rm{Hz}}}$. Inverting this relation gives an expression for the unit second in terms of the defining constant $\Delta\nu_{\rm{Cs}}$: $$1\;{{\rm{Hz}}} = \frac{\Delta\nu_{\rm{Cs}}}{{9\:192\:631\:770}}\ \rm{or}\ 1\ \rm{s} = \frac{{9\:192\:631\:770}}{\Delta\nu_{\rm{Cs}}}$$
2. The effect of this definition is that the second is equal to the duration of ${9\:192\:631\:770}$ periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ${^{133}\rm{Cs}}$ atom.
3. The reference to an unperturbed atom is intended to make it clear that the definition of the SI second is based on an isolated caesium atom that is unperturbed by any external field, such as ambient black-body radiation.
4. The second, so defined, is the unit of proper time in the sense of the general theory of relativity. To allow the provision of a coordinated time scale, the signals of different primary clocks in different locations are combined, which have to be corrected for relativistic caesium frequency shifts.
5. The CIPM has adopted various secondary representations of the second, based on a selected number of spectral lines of atoms, ions or molecules. The unperturbed frequencies of these lines can be determined with a relative uncertainty not lower than that of the realization of the second based on the ${^{133}\rm{Cs}}$ hyperfine transition frequency, but some can be reproduced with superior stability.