Three rational number notations -- fractions, decimals, and percentages -- have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification process theory to account for people's preferences among fractions, decimals, and percentages. According to this theory, the preferred notation for representing a ratio corresponding to a given situation depends on the processes used to quantify the ratio or its components. Quantification process theory predicts that if exact enumeration is used to generate a ratio, fractions will be preferred to decimals and percentages; in contrast, if estimation is used to generate the ratio, decimals and percentages will be preferred to fractions. Moreover, percentages will be preferred over decimals for representing ratios when approximation to the nearest percent is sufficiently precise, due to the lesser processing demands of using percentages. Experiments 1, 2, and 3 yielded empirical evidence regarding preferences that were consistent with quantification process theory. Experiment 4 indicated that the accuracy with which participants identified the numerical values of ratios when they used different notations generally paralleled their preferences. Educational implications of the findings are discussed.

中文翻译：

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人们如何在有理数符号中进行选择？

三种有理数符号——分数、小数和百分比——以现代形式存在了 300 多年，这表明每种符号都有不同的功能。但是，尚不清楚这些函数是什么以及人们如何选择在给定情况下使用哪种符号。在本文中，我们提出了量化过程理论来解释人们对分数、小数和百分比的偏好。根据该理论，表示对应于给定情况的比率的首选符号取决于用于量化比率或其组成部分的过程。量化过程理论预测，如果使用精确枚举来生成比率，分数将优先于小数和百分比；相反，如果使用估计来生成比率，小数和百分比将优先于分数。此外，当最接近的百分比足够精确时，百分比将比小数更适合表示比率，因为使用百分比的处理需求较少。实验 1、2 和 3 产生了与量化过程理论一致的偏好的经验证据。实验 4 表明，参与者在使用不同符号时识别比率数值的准确性通常与他们的偏好平行。讨论了研究结果的教育意义。由于使用百分比的处理要求较低。实验 1、2 和 3 产生了与量化过程理论一致的偏好的经验证据。实验 4 表明，参与者在使用不同符号时识别比率数值的准确性通常与他们的偏好平行。讨论了研究结果的教育意义。由于使用百分比的处理要求较低。实验 1、2 和 3 产生了与量化过程理论一致的偏好的经验证据。实验 4 表明，参与者在使用不同符号时识别比率数值的准确性通常与他们的偏好平行。讨论了研究结果的教育意义。