Acuity of the approximate number system as measured by performance on a non-symbolic numerical comparison task, is a key construct in the numerical cognition literature. The current study examines if performance on the numerical comparison task may be predicted by the precision of numerical representations. We present data from two behavioral experiments and a computational model. In each experiment we consider two hypotheses. First, the hypothesis that accurate numerical comparison is

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... due to precise representations of number. Secondly, we consider that performance in numerical comparison is largely independent of representation precision and relies on variation in decision-making criteria. Behavioral results demonstrate that variation in participants' numerical comparison performance does not correlate with the precision of their numerical representations. Results suggest that changes in the decision-making process can account for variation in numerical comparison performance. Computational modeling results demonstrate how numerical comparison performance does not need to rely on representation precision. We discuss the implications for the relationship between numeracy and outcome measures such as symbolic arithmetic.