= Solution
The <Reynolds number> compares inertial and viscous effects:
$$
\mathrm{Re}=\frac{\rho UL}{\eta},
$$
where $\rho$ is fluid <mass density>, $U$ a characteristic swimming <speed>, $L$ a characteristic body <length>, and $\eta$ the <dynamic viscosity>. Both swimmers are in the same fluid, so the fluid properties cancel from the ratio:
$$
\frac{\mathrm{Re}_{\mathrm{bacterium}}}{\mathrm{Re}_{\mathrm{whale}}}
=\frac{U_bL_b}{U_wL_w}.
$$
For an order-of-magnitude estimate, take $L_b=2\,\mu\mathrm m$, $U_b=20\,\mu\mathrm{m\,s^{-1}}$, $L_w=10\,\mathrm m$ and $U_w=5\,\mathrm{m\,s^{-1}}$. With water values $\rho\simeq10^3\,\mathrm{kg\,m^{-3}}$ and $\eta\simeq10^{-3}\,\mathrm{Pa\,s}$, these give
$$
\mathrm{Re}_b\simeq4\times10^{-5},\qquad
\mathrm{Re}_w\simeq5\times10^7,
$$
and hence
$$
\boxed{\frac{\mathrm{Re}_b}{\mathrm{Re}_w}\simeq8\times10^{-13}\sim10^{-12}}.
$$
The dimensions and swimming speeds are estimates, so this ratio is not a universal species-independent constant. Its physical significance is robust: <viscous forces> dominate the bacterium's motion, whereas fluid <inertia> is crucial for the whale.
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