  We study the weight or compositeness of the $\pi\pi$-$K\bar{K}$ and
$\pi\eta$-$K\bar{K}$ in the composition of the $f_0(980)$ and $a_0(980)$
resonances, respectively. Either we use the saturation of the total width and
compositeness, or we use a Flatt\'e parameterization taking also into account
the spectral function of a near-threshold resonance. We make connections and
compare between these two methods. We take input values for the pole mass and
width from several determinations in the literature. In addition, we take as
third input either the total compositeness or the decay-width branching ratio
to the lighter channel for each resonance. It turns out that for the poles
considered the meson-meson components are dominant for the $f_0(980)$, while
for the $a_0(980)$ resonance they are subdominant. We also provide partial
decay widths and partial compositeness coefficients, so that the $K\bar{K}$
component is the most important one for the $f_0(980)$. Additionally, this
study stresses the need to distinguish between the bare and dressed couplings
and widths in a Flatt\'e parameterization. We elaborate on the connection
between the partial-decay widths calculated in terms of the dressed couplings
and the actual measured ones. Due to the coupled-channel dynamics when the pole
lies near the heavier threshold in the second Riemann sheet some changes are
needed with respect to standard relations.
