A left-c.e. real number \(\alpha \) is \(\rho \)-speedable if there is a computable left approximation \(a_0, a_1, \ldots \) of \(\alpha \) and a nondecreasing computable function f such that we have \(f(n) \ge n\) and $$\begin{aligned} \liminf \limits _{n\rightarrow \infty }\frac{\alpha -a_{f(n)}}{\alpha -a_n}\le \rho , \end{aligned}$$ and \(\alpha \) is speedable if it is \(\rho \)-speedable for some \(\rho 0\).