In a context where the viewer expects a natural number, like 1, 2, 10, or a billion, a number from a larger set, like pi, infinity, three quarters, or negative twelve is used. It's funny because it makes no real-world sense. In formal mathematical jargon, this is a violation of the domain of discourse.
Since it's dependent on what you're trying to count, having "zero" of something may or may not be a non-natural number gag. A zero dollar bill is unexpected, while a politician with zero fans is just sad. Similarly, a half-dollar bill is just fine, even if your country might not issue them, while a politician with half a fan is nonsense.
May be explained in the story, maybe not. Either way, it's supposed to be mathematically correct, unlike Counting to Potato, where nonsense numbers are used because the character communicating them doesn't know how to count right. Compare Eleventy Zillion, where nonsense number names are used to suggest vaguely-defined but very large numbers.
A Missing Floor will often have a fractional number between the numbers of the two floors it's physically inbetween. Minus World and Missing No can cause this to appear in video games. Episode 0: The Beginning and Unusual Chapter Numbers are out-of-universe examples.
- One comic of The Far Side has a mother introducing her 1.5 children. The .5 child is missing one side of his body.
- In the "Logic with Pinkie Pie" fan video, along with several other random numbers, Pinkie claims that there are 3.14159 stars in the sky.
- In Being John Malkovich, Craig takes a job as a filing clerk on floor 7 1/2 of the Mertin-Flemmer Building. It's between the floors ones numbered 7 and 8 and half the height of a regular one.
- The Subtle Art of Not Giving a Fuck joked about kissing your 2.5 kids goodbye (it's joking about how a gallop poll showed 2.5 is considered the average ideal number of children in a family, and pretending that a single family could precisely match that ideal).
- When the Discworld spin-off people were selling official Unseen Academicals football shirts, Ponder Stibbons's shirt number was given as 1.618; the Golden Ratio.
- Train platform 9 3/4 in Harry Potter. It is accessed by walking straight into the wall between platforms 9 and 10, which has been enchanted to act as a portal to the Hogwarts Wizarding School train.
- In The Phantom Tollbooth, Milo learns of a perfectly average family with exactly 2.58 children, among other similar quirks. The 0.58 child doesn't seem to be any worse for the wear, and is the only one who can drive their fractional car.
- In The Legend of Zelda: Skyward Sword, you can find rupoors instead of rupees in some treasure chests. As their name implies, they have a negative cash value. And yes, if Link opens a chest, he will always take the rupoor if there's one inside.
- In the "Claptastic Voyage" DLC for Borderlands: The Pre-Sequel!, Handsome Jack meets up with the Vault Hunters on Deck 13 1/2, a hidden floor between Deck 13 and Deck 14 of Helios.
- In 8-Bit Theatre, Red Mage suggests that if the Light Warriors were to attempt the Dwarven "Bearded Trials", only 1/3 of the Light Warriors would survive. The problem is that there are four light warriors, which would result in 1 and 1/3 Light Warriors surviving per his estimate.
- Arthur, "Arthur's TV-Free Week":
D.W.: Arthur, think of a number between one and ten.
Arthur: Two and a half.
D.W.: That's not a real number!
Arthur: Is too!
D.W.: Is not! Mom, only the numbers one through ten are numbers, right?
Arthur: Why can't I use halves? It's not my fault if she can't do the math.
- A Family Guy Cutaway Gag portrays Two and a Half Men as being about two guys and a third who's missing his lower body who all scream in horror.
- Futurama has plenty of these, due to the amount of mathematicians on the show's staff.
- The TV channel seen the most is Channel Square Root 2.
- Blernsball (the 31st Century version of baseball) players have fractions and equations on their uniforms because all the available whole numbers have been retired.
- There is a pi-th Avenue in New New York.
- The episode "The Late Philip J. Fry" features a parody of the Zager & Evans song "In the Year 2525" which mentions the year 1,000,000 1/2.
- In the Goofy cartoon "How to Play Football", the ball lands right between the goalposts, wobbling back and forth as the gun ending the first half fires. The bullet from said gun deflates the ball, leaving it hanging there. After much deliberation, the officials decide to award it half a point.
- Gravity Falls:
- Quentin Trembly was elected the 9th president of the United States. After he is erased from historical record and replaced with William Henry Harrison, Trembly is referred to as the 8 1/2th president.
- One of Trembly's many acts as president that lead to the US government pretending that he never existed is creating the -$12 bill.
- One artifact the Author picked up in another dimension is the infinity-sided dienote , which when rolled can cause anything to happen.
- The Grim Adventures of Billy & Mandy:
- Billy is stated by his principal to have scored -5 on an IQ test.
- After Fred Flintstone grabs Billy's teacher, she (incorrectly) assumes he was taking her to be his wife. Among her demands is to specifically have 2.5 children.
- Histeria! did a song based on the legend that David Rice Atchison was president for a day. A subtitle identifies him as "The 11 1/2 U.S. President."
- Looney Tunes:
- Combined with Counting to Potato in the Phineas and Ferb episode "Got Game?" At the start of the final game, the score is: Girls — square root of Pi, Boys — a crudely-drawn picture of a duck.
"Clearly, it's still anyone's game."
- The Oblongs: When Pickles' youth group is one member short of the minimum, Pristine snidely comments that Beth being "at most one half" cancels out Helga being "at least one-and-a-half".
- LaTeX and METAFONT are scheduled to make their final releases be exactly version Pi and Sqrt(2), respectively.
- In India, there's an organization that distributes 0 rupee bills. They aren't intended to be used as currency, but rather to shame officials that ask for bribes.
- Exploited by penny shaving fraud, where the thief steals money in fractions of a cent from each transaction. Since the bank statement is supposed to round to the nearest penny, the victim can't see the theft.