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The Collaborative International Dictionary of English v.0.48:

nano- \nan"o-\ (n[a^]n"[-o]-), pref. 1. A prefix meaning one-billionth; as, a nanogram is one-thousandth of a microgram. [PJC] 2. Very small; submicroscopic; -- used to designate sizes smaller than those that would be referred to as micro-; as, nanoscale manipulations. [PJC]
The Jargon File (version 4.4.7, 29 Dec 2003):

nano- pref. [SI: the next quantifier below micro-; meaning ? 10^-9] Smaller than micro-, and used in the same rather loose and connotative way. Thus, one has nanotechnology (coined by hacker K. Eric Drexler) by analogy with microtechnology; and a few machine architectures have a nanocode level below microcode. Tom Duff at Bell Labs has also pointed out that ?Pi seconds is a nanocentury?. See also quantifiers, pico-, nanoacre, nanobot, nanocomputer, nanofortnight.
The Free On-line Dictionary of Computing (30 December 2018):

nano- /nan'oh/ 1. A prefix meaning 10^-9 or one billionth. Used loosely to mean "small", e.g. nanotechnology, or (rarely), following "nanosecond", to mean a short time, e.g. "I'll be with you in a nano". [Jargon File] (2002-03-02)