title: Decimal fraction representations are not distinct from natural number representations - evidence from a combined eye-tracking and computational modeling approach.
abstract: Decimal fractions comply with the base-10 notational system of natural Arabic numbers. Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects) differed in their size between decimal fractions and natural numbers. In the present study, we examined whether these differences indeed indicate that decimal fractions are represented differently from natural numbers. Therefore, we provided an alternative explanation for the semantic congruity effect, namely a string length congruity effect. Moreover, we suggest that the smaller compatibility effect for decimal fractions compared to natural numbers was driven by differences in processing strategy (sequential vs. parallel). To evaluate this claim, we manipulated the tenth and hundredth digits in a magnitude comparison task with participants' eye movements recorded, while the unit digits remained identical. In addition, we evaluated whether our empirical findings could be simulated by an extended version of our computational model originally developed to simulate magnitude comparisons of two-digit natural numbers. In the eye-tracking study, we found evidence that participants processed decimal fractions more sequentially than natural numbers because of the identical leading digit. Importantly, our model was able to account for the smaller compatibility effect found for decimal fractions. Moreover, string length congruity was an alternative account for the prolonged reaction times for incongruent decimal pairs. Consequently, we suggest that representations of natural numbers and decimal fractions do not differ.
authors.affiliation: Knowledge Media Research Center, Tuebingen Germany ; Department of Psychology, Eberhard Karls University, Tuebingen Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Huber
authors.affiliation: Knowledge Media Research Center, Tuebingen Germany ; Section Neuropsychology, Department of Neurology, University Hospital, Rheinisch-Westfälische Technische Hochschule Aachen University Germany.
authors.forename: Elise
authors.initials: E
authors.lastname: Klein
authors.affiliation: Section Neuropsychology, Department of Neurology, University Hospital, Rheinisch-Westfälische Technische Hochschule Aachen University Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Willmes
authors.affiliation: Knowledge Media Research Center, Tuebingen Germany ; Department of Psychology, Eberhard Karls University, Tuebingen Germany.
authors.forename: Hans-Christoph
authors.initials: HC
authors.lastname: Nuerk
authors.affiliation: Knowledge Media Research Center, Tuebingen Germany ; Department of Psychology, Eberhard Karls University, Tuebingen Germany.
authors.forename: Korbinian
authors.initials: K
authors.lastname: Moeller
keywords: artificial neural network; compatibility effect; computational modeling; decimal fractions; number comparison; string length congruity effect
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