  We investigate the efficiency of several types of continued fraction
expansions of a number in the unit interval using a generalization of Lochs
theorem from 1964. Thus, we aimed to compare the efficiency by describing the
rate at which the digits of one number-theoretic expansion determine those of
another. We study Chan's continued fractions, $\theta$-expansions,
$N$-continued fractions and R\'enyi-type continued fractions. A central role in
fulfilling our goal is played by the entropy of the absolutely continuous
invariant probability measures of the associated dynamical systems.
