ABSTRACT
Previous research has shown that multi-digit number processing is modulated by both place-value and physical size of the digits. By pitting place-value against physical size, the present study examined whether one of the attributes had a greater impact on the automatic processing of multi-digit numbers. In three experiments, participants were presented with two-digit number pairs that appeared in frames. They were instructed to select the larger frame while ignoring the numbers within the frames. Importantly, we manipulated the physical size of the digits (i.e., both decade/unit digits were physically larger) within the frames, the unit-decade compatibility (i.e., the relationship between the numerical values of both decade and unit digits was consistent or inconsistent), and the congruity between the numerical values of the decade digits and the frames' physical size (i.e., decade-value-frame-size congruity). In Experiment 1, where all pairs were unit-decade compatible, a decade-value-frame-size congruity effect emerged for pairs with physically larger decade, but not unit, digits. However, when adding unit-decade incompatible pairs (Experiments 2-3), in unit-decade compatible pairs, there was a decade-value-frame-size congruity effect regardless of the digits' physical size. In contrast, in unit-decade incompatible pairs, there was no decade-value-frame-size congruity effect, even when the physically larger digit (i.e., unit) contradicted the place-value information, presumably due to the cancellation of the opposing influences of the digits' physical sizes their place-values. Overall, these findings suggest that place-value and physical size are intertwined in the Hindu-Arabic numerical system and are processed as one.
ABSTRACT
Little is known about the mental representation of exponential expressions. The present study examined the automatic processing of exponential expressions under the framework of multi-digit numbers, specifically asking which component of the expression (i.e., the base/power) is more salient during this type of processing. In a series of three experiments, participants performed a physical size comparison task. They were presented with pairs of exponential expressions that appeared in frames that differed in their physical sizes. Participants were instructed to ignore the stimuli within the frames and choose the larger frame. In all experiments, the pairs of exponential expressions varied in the numerical values of their base and/or power component. We manipulated the compatibility between the base and the power components, as well as their physical sizes to create a standard versus nonstandard syntax of exponential expressions. Experiments 1 and 3 demonstrate that the physically larger component drives the size congruity effect, which is typically the base but was manipulated here in some cases to be the power. Moreover, Experiments 2 and 3 revealed similar patterns, even when manipulating the compatibility between base and power components. Our findings support componential processing of exponents by demonstrating that participants were drawn to the physically larger component, even though in exponential expressions, the power, which is physically smaller, has the greater mathematical contribution. Thus, revealing that the syntactic structure of an exponential expression is not processed automatically. We discuss these results with regard to multi-digit numbers research.
