Summary: Quantitative versions of the central results of the metric theory of continued fractions were given primarily by C. De Vroedt. In this paper we give improvements of the bounds involved . For a real number \(x\), let \[ x \;= \;c_{0} + \frac{1}{\displaystyle c_{1} + \frac{1}{\displaystyle c_{2} + \frac{1}{\displaystyle c_{3} + \frac{1}{\displaystyle c_{4} +_{\ddots}}}}}. \] A sample result we prove is that given \(\varepsilon > 0\), \[ \left (c_{1} (x) {\cdots} c_{n}(x) \right)^{\frac{1}{n}} = { \prod}_{k=1}^{\infty}\left (1+ \frac{1}{k(k+2)} \right)^{\frac{\log k}{ \log 2}} + o \left (n^{-\frac{1}{ 2}}(\log n)^{\frac{3}{ 2}} (\log \log n)^{\frac{1}{2}+\epsilon} \right) \] almost everywhere with respect to the Lebesgue measure.