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Abstract
Although several studies have compared the representation of fractions and decimals, no study has investigated whether fractions and decimals, as two types of rational numbers, share a common representation of magnitude. The current study aimed to answer the question of whether fractions and decimals share a common representation of magnitude and whether the answer is influenced by task paradigms. We included two different number pairs, which were presented sequentially: fraction–decimal mixed pairs and decimal–fraction mixed pairs in all four experiments. Results showed that when the mixed pairs were very close numerically with the distance 0.1 or 0.3, there was a significant distance effect in the comparison task but not in the matching task. However, when the mixed pairs were further apart numerically with the distance 0.3 or 1.3, the distance effect appeared in the matching task regardless of the specific stimuli. We conclude that magnitudes of fractions and decimals can be represented in a common manner, but how they are represented is dependent on the given task. Fractions and decimals could be translated into a common representation of magnitude in the numerical comparison task. In the numerical matching task, fractions and decimals also shared a common representation. However, both of them were represented coarsely, leading to a weak distance effect. Specifically, fractions and decimals produced a significant distance effect only when the numerical distance was larger.
Notes
1We performed one numerical comparison experiment mixing four stimuli types (fraction/fraction pairs, decimal/decimal pairs, fraction/decimal pairs, and decimal/fraction pairs). Results showed that the comparison performance in measures of RTs and accuracy for decimal/decimal pairs was better than that for any of other three types (ps < .001). Accuracy for fraction/decimal pairs was higher than that for fraction/fraction pairs (p = .057). Accuracy for decimal/fraction pairs did not differ from those for fraction/fraction and fraction/decimal pairs (ps > .126). Responses for fraction/decimal pairs were faster than those for fraction/fraction and decimal/fraction pairs (ps < .001). Responses for fraction/fraction pairs did not differ from those for decimal/fraction pairs (p = 1.000). These findings showed that a decimal is more easily processed than a fraction and that fractions are likely to be transformed into decimals.