How many is a zillion? Sources of number distortion

Lance J. Rips*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing that log-like positioning is a consequence of 2 factors: the bounded nature of the number line and greater uncertainty about the meaning of the larger, less frequent number words. Two experiments likewise show that even college students produce log-like placements under the same 2 conditions. In Experiment 1, participants identified positions on a number line for a set that included both conventional and fictitious numbers (e.g., a zillion). In Experiment 2, participants did the same for conventional numbers that included some larger, unfamiliar items (e.g., a nonillion). Both experiments produced results better fit by logarithmic than by linear functions.

Original languageEnglish (US)
Pages (from-to)1257-1264
Number of pages8
JournalJournal of Experimental Psychology: Learning Memory and Cognition
Issue number4
StatePublished - Jul 1 2013


  • Number concepts
  • Numerical reasoning
  • Representations of mathematics

ASJC Scopus subject areas

  • Language and Linguistics
  • Experimental and Cognitive Psychology
  • Linguistics and Language

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