Units of the metric tensor or how to get the unit right for the line element

Question

In this answer it is stated that the metric tensor elements have no physical unit, i.e. $[g_{\mu\nu}] = 1$. What is the convention to get the physical unit of the line element $ds = g_{\mu\nu}dx^\mu dx^\nu$ right. I assume that $[dx^0] = s$ (seconds), and $[dx^i] = m$ (meter) for $i=1,2,3$. The flat spacetime, $$ ds^2 = -c^2dt^2 + dx^2+dy^2+dz^2$$

would suggest that $[g_{00}] = [c^2] = (m/s)^2$.

What is a (the) convention to get the units right.

Answer 1

The typical convention is $x_0=ct$, so $[dx_0]=[dx_i]=~\rm m$.

Although people frequently set $c=1$ to simplify things, and then the whole point is moot.