We study the impact of using mixed and variable numerical precision in the high-order ADER-DG method for solving partial differential equations. The impact of precision on both the overall convergence order, as well as specific sections of the code are examined. This lets us judge how sensible each part of the algorithm is to small losses of precision.We also research how numerical precision affects the stability of ADER-DG by simulating two stationary but numerically challenging scenarios and check whether variable precision can resolve stability issues.Finally, we review the effects of numerical precision on the features Lagrange interpolations, which are commonly used but are susceptible to small changes in the nodal values.