The number decision task: Investigation of the representation of multi-digit numbers

The ability to process multi-digit numbers is an essential skill which we investigated using a number decision task. Subjects were asked to decide whether a target number (e.g., 649) is too small or too large to be the mean between two delimiter numbers that constituted the interval (e.g., 567 and 715). Three-digit numbers were presented vertically with (1) growing interval sizes (i.e., distance between the two delimiters; e.g., interval size between 567 and 715 is 148) and target gap to the mean (e.g., the gap between the 'real' mean 641 and the target 649 is 8) and (2) growing interval sizes with constant gap to the mean (i.e., for each interval size the gap between target and mean was held constant). The results showed that target gap to the mean "masked" the influence of interval sizes, i.e., subjects' performance improved with increasing interval sizes (distance effect). This effect was reversed when constant target gaps to the mean and growing interval sizes were presented. These results were replicated presenting the numbers horizontally and with two-digit numbers. Additionally, a significant influence of decade but no effect of unit compatibility on reaction times and error rates, on number magnitude (size effect) and response format was found. Overall, we showed that the number decision task is an efficient tool to investigate multidigit number representation and the results from the experiments revealed evidence for a hybrid model of multi-digit number representation in which numbers are represented as a whole but also on separate mental number lines that interact with each other.