Despite their importance in public discourse, numbers in the range of one million to one trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Common conceptions of the number line suggest a logarithmic compression of the numbers (Dehaene, 2003). Theories of abstract concept learning suggest that in situations where direct experience is unavailable, people will use the structure of notation systems as a proxy for the actual system. (Carey, 2009; Landy & Goldstone, 2007). Evaluations across two subject populations largely matched the predictions of the latter account. Approximately 40% of participants estimated one million approximately halfway between one thousand and one billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Very brief training procedures proved partially successful both in correcting number line placement and in shifting participants’ judgments of geopolitical situations. These results reinforce notions of abstract concepts as grounded in external notation systems, as well as having direct implications for lawmakers and scientists hoping to communicate effectively with the public.