The cognitive processes involved in the human ability to understand and use positional notation (i.e., place-value) were investigated in a series of psychological experiments. Although the tasks used in all studies were very simple, usually only requiring the tested individual to identify the larger of two numbers as quickly as possible, a number of unintuitive results were obtained. For example, in two digit number comparison, skilled adults' decision times are affected by the ones-place digit even when the tens-place digit is logically sufficient to determine the correct response (e.g., is 48 less than or more than 55?). However, when the number of places is a sufficient cue to answer the question (is 735924 more or less than 5000?), insignificant place information is not extracted. Memory for numbers was also shown to be affected by place-value information. Surprisingly, speed of understanding the relative value of numbers is slowed when the numerical value conflicts with the relative physical size of the numerals. Overall, several physical and symbolic factors strongly influence our ability to understand, manipulate, and remember numbers. (Author)