The expressiveness principle for visualization design asserts that a visualization should encode all of the available data, and only the available data, implying that continuous data types should be visualized with a continuous encoding channel. And yet, in many domains binning continuous data is not only pervasive, but it is accepted as standard practice. Prior work provides no clear guidance for when encoding continuous data continuously is preferable to employing binning techniques or how this choice affects data interpretation and decision making. In this paper, we present a study aimed at better understanding the conditions in which the expressiveness principle can or should be violated for visualizing continuous data. We provided participants with visualizations employing either continuous or binned greyscale encodings of geospatial elevation data and compared participants’ ability to complete a wide variety of tasks. For various tasks, the results indicate significant differences in decision making, confidence in responses, and task completion time between continuous and binned encodings of the data. In general, participants with continuous encodings were faster to complete many of the tasks, but never outperformed those with binned encodings, while performance accuracy with binned encodings was superior to continuous encodings in some tasks. These findings suggest that strict adherence to the expressiveness principle is not always advisable. We discuss both the implications and limitations of our results and outline various avenues for potential work needed to further improve guidelines for using continuous versus binned encodings for continuous data types.