Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The ordinal number matching the number one billion in a series.
 n. One of a billion equal parts.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. The ordinal form of the number one billion.
 n. The person or thing in the billionth position.
 n. One of a billion equal parts of a whole.
from The Century Dictionary and Cyclopedia
 Coming last in a set of a billion terms: an ordinal numeral.
 Being one of a billion equal parts.
 n. One of a billion equal parts; the quotient of unity divided by a billion.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. the ordinal number of one billion in counting order
 n. one part in a billion equal parts
 n. position 1,000,000,000 in a countable series of things
Etymologies
Sorry, no etymologies found.
Examples

In the meantime, a few weeks ago, I watched The Sound of Music (for the billionth time).
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When it was announced a couple of weeks ago that Flickr, the photohosting site, had hosted its five billionth picture, someone pointed out smugly that Facebook already has over three times that number.

There is much significance made of the "first living cell", but the simplest replicating units discovered so far are actually ribozymes (RNA enzymes) which have less than a billionth as many atoms as a cell (a cell is a few quadrillion atoms, while a ribozyme is a few tens of thousands, if I understand correctly).

Apple is counting down to its billionth app downloaded.

The company says its App Store is approaching one billionth download.

Google uses perhaps onebillionth of Watson's resources, or less, to handle each query.

At the end of the billionth cycle, precisely on the dot, the pair, alone in a field of a thousand, began to step forth, from one piece of debris to the next.
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And ever since that fleeting moment, that one billionth of my lifetime, a mere thought, base though it was, it pops into my head every now and then and makes me feel like the son of Sam of sexual perversion.

The portion of what we could see would be much tinier than a layer of paint, or less than one billionth of the known frequencies of light in the Universe.

As Joerres said, it isn't the iPad, but the "10 billionth" ap that is downloaded.
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