In this paper we explore the influence of students' personalized notion of "small" numbers based on real life experiences on their understanding of limits. Tests were conducted on two samples of students. The first sample, consisting of students in the XII grade, had been taught limits using an informal approach (i.e., without recourse to the [epsilon]-[delta] definition) and the second sample, consisting of first year undergraduates, had been taught the formal [epsilon]-[delta] definition of limits. Our research points out that most students in "both" samples round off to zero such "small numbers" while evaluating limits wherever such numbers might occur because they perceive limit as a process of approximation.