Perceiving the “Smallest” or “Largest” Multidigit Number: A Novel Numeric-Scale End Effect

The ability to recognize the smallest/largest objects or numbers in our environment is an essential cognitive skill, however, little is known about perceiving multidigit numbers as end-values. The present study examined end effects in multidigit numbers and whether such effects are impacted by number length, which captures the numeric scale (e.g., 10’s, 100’s). Across four experiments (N = 120, 100, 80, and 120, respectively), participants performed three types of numerical comparisons: same-scale comparisons between end-values and nonend-values (e.g., 100 vs. 200), different-scale comparisons between end-values and nonend-values (e.g., 1,000 vs. 200), and same-scale comparisons of nonend-values (e.g., 300 vs. 200). The type of the end-value (i.e., lower/upper) and overall numerical range used in each experiment varied. The results revealed: (a) a novel numeric-scale end effect, characterized by a relatively small end effect for comparisons between nonend-values and end-values from an adjacent numeric scale, and a larger, consistently sized end effect for comparisons between nonend-values and end-values from nonadjacent numeric scales (≥2 scales), (b) absent or weak end effects in same-scale multidigit number comparisons, and (c) replication of the lower end effect for single-digit comparisons to the end-value 1. These results reveal differential processing of numbers from adjacent versus nonadjacent numeric scales. We rule out a psychophysical explanation for our findings and instead provide a syntactic explanation based on the perceptual dominance of the numeric-scale component and the way it manifests in the counting process. We conclude that a number’s scale plays a crucial role in evaluating multidigit number magnitude.