Common magnitude representation of fractions and decimals is task dependent.

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.