The following technical report is available from http://aib.informatik.rwth-aachen.de: Quantitative Testing Henrik Bohnenkamp, Marielle Stoelinga AIB 2008-01 We investigate the problem of specification based testing with dense sets of inputs and outputs, in particular with imprecision as they might occur due to imprecise measurements, numerical instability or noisy channels. Using quantitative transition systems to describe implementations and specifications, we introduce implementation relations that capture a notion of correctness "up to epsilon", i.e. that allow deviation of the implementations behavior from that of the specification as long as it does not deviate more than epsilon. The deviations are described as Hausdorff distances between certain sets of traces. The implementation relations are conservative extensions of the well-known ioco relation. We develop a testing algorithm that we show to be sound and exhaustive with respect to the implementation relations introduced.