  We determine the leading digit laws for the matrix components of a linear Lie
group $G$. These laws generalize the observations that the normalized Haar
measure of the Lie group $\mathbb{R}^+$ is $dx/x$ and that the scale invariance
of $dx/x$ implies the distribution of the digits follow Benford's law, which is
the probability of observing a significand base $B$ of at most $s$ is
$\log_B(s)$; thus the first digit is $d$ with probability $\log_B(1 + 1/d)$).
Viewing this scale invariance as left invariance of Haar measure, we determine
the power laws in significands from one matrix component of various such $G$.
We also determine the leading digit distribution of a fixed number of
components of a unit sphere, and find periodic behavior when the dimension of
the sphere tends to infinity in a certain progression.
