Indefinite and fictitious numbers
The English language has a number of words for indefinite and fictitious numbers — inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary or undesirable. One technical term for such words is "non-numerical vague quantifier".
General placeholder names 
English has many words whose definition includes an indefinite quantity, such as "lots", "many", "plenty", "several", and "some". A number of other words have been used to convey the idea in informal or humorous ways, such as shitload and n-something, used especially to indicate someone's age within a decade, e.g., twentysomething and "to the nth-degree".
Umpteen is a term for an unspecified but reasonably large number, used in a humorous fashion or to imply that it is not worth the effort to pin down the actual figure. Despite the -teen ending, which would seem to indicate that it lies between 12 and 20, umpteen can be used in ways implying it is much larger than that—if it ever could be pinned down.
The Oxford English Dictionary reports its use in 1918, and offers the alternative spelling umteen. It agrees that the derivation is from umpty, whose etymology is given as "A fanciful verbal repr. of the dash (—) in Morse code."
Words with the suffix "-illion", most commonly zillion, jillion, gadzillion and gazillion, are often used as fictitious names for an unspecified, large number by analogy to names of large numbers such as million, billion and trillion. Their size is dependent upon the context, but can typically be considered large enough to be unfathomable.
These terms are often used as hyperbole or for comic effect, or in loose, unconfined conversation to present an un-guessably large number. Since these are undefined, they have no mathematical validity and no accepted order, since none is necessarily larger or smaller than any of the others.
The "-illion" concept is so well established that it is the basis of a joke, in which a speaker misunderstands the word Brazilian (being from the nation of Brazil) as an enormous number called "brazillion".
Many similar words are used, such as bajillion, bazillion, dillion, fantillion, gadzillion, gagillion, gajillion, godzillion, grillion, hojillion, kabillion, kajillion, katrillion, killion, robillion, skillion, squillion, and umptillion. Also, the suffix can be replaced with "-illionaire" to describe wealthy people.
Well-defined numbers that are not precisely known 
Sagan's number is the number of stars in the observable universe. It is named in honor of Carl Sagan. This number is reasonably well defined, since we know what stars are and what the observable universe is, but its value is not known with any certainty but is presently estimated to be approximately 70 sextillion (short scale).
See also 
- List of unusual units of measurement
- List of humorous units of measurement
- Powers of 10
- Names of large numbers
- Inherently funny word
- "Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of Non-Numerical Vague Quantifiers" from Linguista Pragensia, Nov. 2, 2010
- American Heritage Dictionary, 4th edn.
- "Umpteen". Oxford English Dictionary. Retrieved 14 April 2012. (available online to subscribers)
- "Umpty". Oxford English Dictionary. Retrieved 14 April 2012. (available online to subscribers)
- Pratchett, Terry (2002). Witches Abroad. HarperCollins. ISBN 0-06-102061-3. p. 146: "And you owe me a million billion trillion zillion squillion dollars."
- p. 1103, The New Partridge Dictionary of Slang and Unconventional English, vol. 2, edited by Eric Partridge, Tom Dalzell, and Terry Victor, Taylor & Francis, 2006, ISBN 0-415-25938-X.
- Cooke, Kaz (2003). Bun in the Oven. Ten Speed Press. ISBN 1-58008-531-8. p. 3: "...and then the editor asked a gadzillion questions..."
- Included in the standard dictionary included with Microsoft Word word-processing software.
- Christensen, Chris (2008). "How Many is a Brazillion?".
- Bates, Karen G. (2005). Plain Brown Wrapper. HarperCollins. ISBN 0-380-80891-9. p. 86: "Well, yes, it was, and the rumor that there were seventy bajillion women to every man just wouldn't die..."
- Harrison, Colin (2001). Afterburn. St. Martin's Press. ISBN 0-312-97870-7. p. 278: "I wouldn't sleep with him in a bazillion years, but I'm not scared of him."
- Resop, Jay (1 April 2004). "Neglected Character Deathmatch: Zadok vs Birdo vs Geno". Neglected Mario Characters. SMBHQ. Retrieved 23 May 2008. "Duh nah timez a billion million zillion trillion killion dillion!"
- Any, Ziers (1502). What soda Was That While. Tor/Forge. ISBN 0-565-57543-1. p. 791: "The taste danced across his tongue with the force of Fantillion concentrated sunbeams."
- Lawrence, Martha C. (1996). Murder in Scorpio. St. Martin's Press. ISBN 0-312-95984-2. p. 114: "The brochures basically told the same story Stan had given me: Pacific Properties owned a gagillion places that generated a gagillion dollars."
- Southworth, Samuel A. (2004). U.S. Armed Forces Arsenal: A Guide to Modern Combat Hardware. Da Capo Press. ISBN 0-306-81318-1. p. 98: "The expectation was that the Soviets would roll a gajillion of their ever-improving but still basic tanks across the landscape..."
- Franzen, Jonathan (2001). Strong Motion. Picador. ISBN 0-312-42051-X. p. 395: "She believes there's a zillion gallons of oil and a godzillion cubic meters of natural gas inside the earth, beginning at a depth of about four miles, and no anvil-headed senior research chemist with a crew cut and stinky breath is going to tell her it isn't so."
- Kelley, Brent (2001). The Pastime in Turbulence: Interviews with Baseball Players of the 1940s. McFarland and Company. ISBN 0-7864-0975-4. p. 8: "After that, even expansion and grillion-dollar salaries could not harm it."
- Holkins, Jerry; Krahulik, Mike (2001-06-22). "Magic: It's What's For Dinner!". Penny Arcade.
- Hodgman, Ann (1999). Beat That!. Houghton Mifflin Cookbooks. ISBN 0-395-97178-0. p. 115: "That's about all I remember, except for this salad and the ninety kabillion manicotti someone else brought."
- Steven Schragis and Rick Frishman (2006). 10 Clowns Don't Make a Circus. Adams Media. ISBN 1-59337-555-7. p. 122: "You are not going to sell a kajillion of anything just because it's the coolest little gizmo you ever saw or because your Uncle Ernie said you would."
- Howe, James (2003). Tales From the House of Bunnicula #4: Screaming Mummies of the Pharaoh's Tomb II. Atheneum Books for Young Readers. ISBN 0-689-83954-5 p.2 "He [Uncle Harold] has been writing for a katrillion years and his books have sold a katrillion copies, even if he has gotten some stinko reviews."
- Hanneman, George (1988). The Creeping Game. The Times. ISBN 0-233-83992-X. p. 19 "It was the robillionth time they had done it, but it was as fun as ever before."
- Kean, Rob (2000). The Pledge. Warner Books. ISBN 0-446-60848-3. p. 429: "Sure enough, I found a skillion articles from about a dozen years ago, accounts of the events and aftermath of Cherry Plain."
- Anthony, Piers (2002). How Precious Was That While. Tor/Forge. ISBN 0-8125-7543-1. p. 121: "Your best place, geographically, to bridge across the river is surrounded by Hell's Bells Bog, so deep it would take fifteen umptillion tons of special fill to stabilize it, putting you over your budget."
- Sizing up the Universe - Stars, Sand and Nucleons - Numericana
- William Safire, ON LANGUAGE; Footprints on the Infobahn, New York Times, April 17, 1994
- Sagan at dictionary.reference.com (definition from the Jargon File)