Neon Genesis Evangelion suffers from this. All the Techno Babble related to the Evas (especially in the "Ritsuko shouts at a monitor and defeats the Angel" episodes) is given without units ("It's decreased by 0.3!"), although they do occasionally remember to use units for things like sizes. There's also plenty of cases of unitless numbers stated to absurd degrees of precision and probability calculations involving complete unknowns.
Units were lobbed off and scales not even mentioned whenever possible in regards to the titular cyborgs in order to justify drawing them to wildly-varying Rule of Cool proportions (which is negated once you realize human pilots stand next to the Evas quite frequently). To balance this out, numbers that were of absolute importance to the plot that actually had units - "5 minutes" of internal battery power - didn't matter either.
The talking computer (or whatever it is) in Voices of a Distant Star does this a few times, saying that enemy units are "at twenty thousand" or similar things. It isn't even all that clear what type of unit this is; it's probably a distance, but it could be the number of uneaten sandwiches they have in storage, for all we know.
In Bleach, Captain Yamamoto's Bankai has an ability that allows him to revive every person he's ever killed as an army of black skeletons. How many people has he evidently killed? Ten trillion, or so it's said. For reference: this is about a hundred times more than the estimated number of people to have ever lived at a mere 106 billion.
Arguably, this is a case of Unreliable Narrator at work. The user is the one claiming there are 10 trillion of them (The name of the technique translates as "Grand Array of the 10 Trillion Burning Corpses") - just because it has an overly showy name doesn't mean there are actually that many.
Also in fairness, the man has been alive for well over a millennium and regularly does battle with creatures that are themselves gestalt entities composed of thousands of souls. Obviously not ten trillion souls, but a damn lot of them all the same.
Dragon Ball is infamous for its training sessions. During such, characters commonly train with things like weighted clothing and increased gravity. Doesn't sound so absurd? Well, considering even relatively early in the series characters were able to shatter mountains and create huge lake sized craters with a single blow..... Let's just say wearing a few tons on each arm wouldn't really equate to such force.
Galactus is often called the "slayer of millions", when he has been devouring inhabited worlds at a rate varying from once a century (early in his life) to once a month (more recently) since shortly after the Big Bang. This is... technically correct, but not really indicative of the real scale of things. Even if the "millions" is a count of worlds, he would already be well into the billions by now.
There are about 7200 Green Lanterns to patrol the entire Universe. Considering how big 1/7200th of the Universe is, it is little wonder the Green Lantern Corps has failed to stamp out evil in the cosmos: sheer lack of manpower. The fact that in the DCU, the vast majority of the Universe is devoid of life helps a bit, but not by that much.
Partly Science Marches On; at one time the phrase "island universe" was used to mean what we would today call a "galaxy". When DC asked Larry Niven to write the Green Lantern "Bible", one of the assumptions he made was that the Guardians were just arrogant (that's not the assumption part, that's pretty much a given) and called the Milky Way galaxy "the universe". This reduces the size of a sector by a tremendous factor, but it's still pretty darn big.
DC Comics has several instances where the writer hilariously misunderstands how the decibel scale of measuring sound works, and the workings of sound in general. Firstly, the decibel scale is logarithmic, which means that an increase of ten decibels means the sound and the energy carried by the soundwave is ten times stronger. 200 decibels in fact means a sound that is ten billion times as strong as a sound of 100 decibels. Let's establish some benchmarks here: At 194 the sound exerts pressure roughly equal to atmosphere at sea level. 200 decibels is normally lethal to humans, and is more a shockwave than a soundwave. The epicenter of man-made explosions ranges around 200-300 decibels. Got all that? Good. Let's take a look at some examples where this is grossly mishandled.
The strength of Black Canary's canary cry has several times been stated as being 300 decibels, which is much more than the shockwave you get from a good-sized nuclear explosion. People who have been hit it have just been thrown around some and survived with minor injuries, while in fact they should have been reduced to a thin red mist.
Pre-Crisis Superboy helps out a scientist who wants to measure the loudest sound he can create. Superboy complies by first providing five thousand decibels, which probably would be more than enough to reduce the entire planet to dust. Then he one-ups himself by one million decibels.
Finally, in New Teen Titans Cyborg casually blasts an enemy in combat with "one million decibels of white noise".
In The Prayer Warriors, a meeting of "Secret Christians" at Hogwarts has hundreds of attendees from the school. Hogwarts has only 280 students.
In Stealth, one of EDI has somehow downloaded "all the music on the Internet". The theoretical sum of all music on the Internet would be measured in petabytes, if not exabytes, and would require a hardware mainframe hundreds of times larger than EDI himself. It would take him days upon days to download it all, even assuming the fastest possible Internet connection speed.
Or, if you packed it all onto 1TB zip-drives, an SUV trunk. Last I checked (Nat-Geo Summer 2013 IIRC), the entirety of the Internet was only a little over ten Petabytes (10,000 TB). At a volume of approximately 3cc each, a bit more than a tenth of a cubic meter. (That's less than a cubic foot for those of us who use that system).
Event Horizon messes has quite a few lines which contain physics whoppers that can spoil its Cosmic Horror mood. The Lewis and Clark is a space ship which develops a breach in the hull. Smitty claims that the ship has 218 liters of air left. But a body of gas fills up however much space the container that holds them has, meaning they should have measured how much was left in mass or pressure. Additionally, 218 liters is not a very large volume. It's approximately forty-five gallons, which would fit in about a fifth of a cubic meter. In other words, a space about three feet long by three feet wide by a little more than half a foot deep. It seems that Smitty is talking about the air in the cabin, which has a volume roughly equivalent to that of a small ranch house. If 218 liters of air under earth-like atmospheric pressure then expanded to fill that space, anyone without a sealed space suit (like Smitty) would be dying of irreconcilable pressure and temperature differences. If the ship stored reserve air, expanding that air from 218 liters to the size of the cabin would cause it to become very, very cold very fast, just like a can of pressurized air for cleaning electronics does when you lower the pressure quickly.
In Isaac Asimov's Foundation series, the planet Trantor is stated to have a surface area of 75 million square miles, and a population "in excess of forty billions". That puts the population density somewhere between 533 and 666 people per square mile. This is LESS than the average suburb, yet Trantor is described as being a teeming planet-wide city.
The average suburb is not self-contained. If you add in all the businesses, workplaces, industry, transportation and other infrastructures required to do that... it will start to feel rather more crowded.
Cities (which contain all those things) are far far denser than suburbs. Manhattan is a hundred times denser than that, the whole of Los Angeles has a density of over ten times that. So no, still plenty sparse.
Asimov also indicated that the structure of Trantor extended more than a mile underground and up to several hundred stories above ground. Taking into account the additional area therefore available, which may be a few hundred times the land area, the problem with Trantor isn't overcrowding, it's finding someone else to talk to face to face.
Unless you use the largenote properly termed "long scale" version of billion - that is, what is commonly called a trillion nowadays. In which case you really do need hundreds of stories above and below ground to cram half a million people into every square mile.
Isaac Asimov's Caves of Steel takes place "thousands of years in the future", where Earth is overpopulated and all Earthmen are crowded into domed Cities in cramped quarters. The world population at that point? 8 billion. (In real life, we reached 7 billion in 2012 and are on track to hit 8 billion in 2025.)
In Starship Troopers, the Terran Federation Army (the Mobile Infantry), claims to be 10,000 strong. Even if the entire army were all assaulting one world (extremely unlikely), Earth has a land mass of 149 MILLION square kilometers. If the entire force were dropped on a world of similar size, that would leave them 14,900 square kilometers EACH - or a plot of land 122 x 122 km for a single soldier. On worlds that are bigger, or contain less than 2/3 of their land mass under water, that figure would be considerably larger per man.
This is. . . probably intended. At one point in the book, they pack in the Mobile Infantry at such incredibly close range that individual troopers are only a mile or so apart. It's treated as terrifying close together and at massive risk of friendly fire, and the main character says outright that this is as bunched up as they can possibly get without guaranteeing killing each other. Mobile Infantry are incredibly powerful and they tend to spam nuclear warheads like candy.
The 10,000 figure is a single division and multiple divisions are mentioned so they have way more than just 10,000 troops.
In Farscape Zhaan claims to have searched planets for three people in hiding, over a period of time roughly equivalent to 20 days. They also mention how completely ridiculous the chances of finding them actually are, so maybe it's just supposed to show how desperate she was.
Most battles in Babylon 5, even planetary bombardments, only have a few thousand deaths. The only one with a more than a million had asteroids, and that took weeks of nonstop dropping). One of the canonical novels says that 600 million Narns died in the bombardment, however in Season 3 Straczynski said that only '5 or 6 million' Narns had died, which seems preposterously unlikely.
Throughout Star Trek, unit numbers fluctuated wildly between the various series. The original series said there were only 12 Constitution-class ships, and showed little evidence of any others on Starfleet's possession; in The Next Generation there were initially only six Galaxy-class ships built, with another six on order, and a loss of 39 vessels against the Borg at Wolf 359 was apparently a total catastrophe that crippled Starfleet. By Deep Space Nine the Federation was regularly committing as many as six hundred ships at a time to individual battles with the Dominion; and in response to questions about the unexpectedly-high registry numbers of Voyager and Defiant, Ronald Moore went on record as saying that Starfleet probably had at least thirty thousand ships. One could assume that Starfleet registries cover everything from Starships to shuttles to orbital transports, which might help matters some.
When it was written, the Battle of the Wolf was supposed to be a massive loss of Starships, until people wrote in concerning this trope. It was later Retconned to be only the fleet stationed on Earth itself, and the tragedy was that those were 39 of Starfleet's best ships with their best crews. It would be similar to Britain losing the entire Royal Guard to a single enemy ship. Numerically, it wouldn't significantly harm the army, but it would be a massive psychological blow.
In truth, nobody ever actually says in any episode or film that Wolf 359 crippled Starfleet, or even came close to doing so. When they reach the scene of the battle everybody reacts to the loss as if it was a major disaster, but at the end of the episode Shelby smilingly announces that they will have the "fleet back up in less than a year." So it really does seem as if the primary impact was a psychological one.
If you think about it, it doesn't even really matter how many ships Starfleet has in total. The point is that 40-odd ships were believed by Starfleet themselves to represent a real deterrent even to a powerful enemy, yet a single Borg ship destroyed 39 ships and cost 11,000 lives while barely slowing down. Dialogue indicates that Starfleet assembled the fleet at Wolf 359 in a hurry, in days at most, and there was was no time to assemble a bigger fleet. Whether Starfleet had only 40 more ships or 40,000, there was no way to get them assembled in time to stop the Borg attacking Earth. It's not a case of "my god, they've destroyed the entire fleet", it's a case of "my god, what the hell do we do now?". Shelby's line at the end of the episode suggests that physically replacing 39 ships or even 11,000 active Starfleet personnel wouldn't actually be that challenging.
Gene Roddenberry also seems to have had a bit of a blind spot with the number 1. A Star Trek: The Original Series episode reported viewscreen magnifications of "1 to the fourth power" and so onnote Conceivably Fan Wankable as the truncated way that 23rd-century English expresses scientific notation, i.e. they chop out the "times ten" part, but that is making the Author's Saving Throw for him. (Poor throw, too, since it'd be far easier to say "magnification 10,000".). In his original pitch, Roddenberry reinvented Drake's Equation (he didn't have the actual equation on hand) to show how likely alien life was, and ended up with terms raised to the first power.
Selas' grand plan to invade Vulcan...with a grand total of 2000 troops. That's barely enough to invade a single town much less than a entire planet (granted, orbital superiority is a force multiplier, but that's dependent on the defenders not having ships of their own). She then lauds that they'd be nearly impossible to discharge since they had been 'dug in' by the time Starfleet responds.
In "The Royale", the temperature is given as -291 Celsius. That's below absolute zero, which is to say, take the coldest physics will allow it to be, then get about 18 degrees colder.
In Star Trek S 1 E 23 A Taste Of Armageddon, a weapon directed at the Enterprise has "18 to the 12th power decibels". The fact that a sonic weapon is being used in space can be rationalised as it just being a low frequency weapon of some sort. The real problem is that decibels is a logarithmic scale, so the number quoted is 1 followed by 1156831381426176 zeroes times a reference power (often 1 milliwatt). For perspective, the entire luminous output of the observable universe is only 2x10^49 Watts.
In one of the background books, it is mentioned that it took around 20 years to pacify a sector with the combined strength of a Crusade and that this is a remarkably short time.
On the other hand, the Macharian Crusade is said to have taken seven years and pacified over a thousand worlds for the Imperium. Even if a lot of the planets surrendered without a fight, that's still at least a whole planet every other day for seven years. (Then again almost all of those worlds revolted not long after)
Several planetary wars are often played out in a matter of weeks or months. World War 2 took a good few years to finish. However there are some justifications, the biggest of which is that most of these are global campaigns, which are global events real players can participate in. It would seriously suck to have to wait 4-5 years for the results of a summer event.
40k has also been noted for having a particular fondness for the Elites Are More Glamorous and Keystone Army tropes: an average Space Marine victory involves around twenty five Marines assassinating a planetary governor to make the entire rest of the planet surrender immediately. In the few cases in which the writers are able to get away from that particular comfort zone, we start to get less egregious scenarios - such as the novel Fire Caste, where a planetary siege has been waging back-and-forth for decades.
Eldar Craftworlds are another case of writers not having any set guidelines, resulting in wildly contradictory statements about their size and populations. Gav Thorpe, who wrote the Eldar-centric "Path of the..." books, said he envisioned largest Craftworlds having habitable area the size of a continent with population of low millions, because apparently having tens of millions of Eldar on a Craftworld would seem too big for a dying race. Even if the population of every Craftworld would be in hundreds of millions, all Craftworld Eldar in the entire Galaxy (no exact number of Craftworlds have been given, but when the background gives a ballpark number it's usually "hundreds") would have the total population of maybe 3 or 4 Imperial hive worlds (which can have population of hundreds of billions each). Phil Kelly, who wrote the Eldar and Dark Eldar codices, on the other hand seems to place the population of Craftworlds as much higher, since some of the background he's written would suggest even a small Craftworld would have a population of several million.
Recently Mat Ward's Craftworld Iyanden supplement, which states the pre-tyranids attack population (always stated to have the largest) in the billions. Then again, Ward's popularity among hardcore 40K fans is midway between scurvy and a personal encounter with Tyranid cortex leeches; it's quite possible he didn't care.
And of course, considering this is a race with galactic influence that regularly engages in battles with a dozen galactic powers, and with each being effectively continent-sized (sometimes moon sized) cities, one has to wonder why even given a number of billions you see so much population density whenever there's a shot of the inhabited sections of the craftworlds (skyscrapers with numerous vehicles flying around them), or how they manage to be in so many conflicts at once and popping out enough new Eldar to replace all the casualties (if they manage to be a dying race for thousands of years with a population of millions for a single craftworld, yet that craftworld still engages in many wars and skirmishes every year... low population that fights a lot that's still somehow only slowly declining over a course of millennium means high replacement rate, pretty un-Eldar-y!). On a galactic scale, even hundreds of billions or trillions would be a very small drop in the bucket well fitting for a 'dying race,' that used to be Imperium big, it only sounds big to those used to a single planet population like Earth, leaving us with population numbers in the millions to billions that are hilariously tiny for what they regularly manage to accomplish and the body counts they accrue during it.
Only the Planetville nature of the BattleTech universe combined with its quasi-feudal nature can really explain how, given the bottleneck of interstellar travel, any major planet ever changes hands as the result of an invasion. The thought of using some non-microscopic fraction of the industrial capacity of a world to create a defensive force that would simply swamp a few dozen 'Mechs dropping out of the sky by weight of numbers is never seen to enter anybody's mind.
One of the ways that the game rules attempt to justify this is that it takes significantly more damage to disable a BattleMech than another vehicle of comparable tonnage. A "decent anti-tank rifle" will accomplish squat against a 'Mech under the rules, as a well-armored 'Mech can shrug off dozens of anti-vehicle missiles without suffering systems damage. Realistic? No, but it does serve the purpose of the game (giant robots pounding away at each other) better than more realistic rules would.
Ironically, the rules (especially in but not limited to the Total Warfare edition) then do in fact allow infantry to do fairly significant damage to 'Mechs that happen to carelessly wander into range of their weapons. A stock twenty-odd man Inner Sphere ballistic rifle platoon can hit for upwards of ten points of damage per turn, all in annoying little 2-point critseeker damage packets. They're slow and not a major threat over open ground where 'Mech weapons can pick them off from a safe distance, but infantry are one of the legitimate reasons few Mech Warriors look forward to urban combat among other things — and these are just a bunch of warm bodies with man-portable weapons who don't even have a single half-decent cheap combat vehicle to their name yet.
Star Wars is incredibly prone to presenting an inaccurate sense of scale.
There obviously wasn't much coordination between the writers, since the EU droid numbers were in the quintillions ...
In Shatterpoint, Mace Windu points out that the million-odd clones work out to roughly one per system, and suggests that the majority of the fighting, especially in the less-critical areas, is being done by regular militia forces.
Meanwhile, there often seems to be only one military academy - admittedly one which takes up most of a planet - for the entire galaxy. For comparison, there are four in the USA alone, and that's not counting the three major service academies. (The sourcebooks explain that there's actually one academy per sector (roughly, one per every 1000 inhabited planets), but good luck getting the writers to pay attention to that ... )
The official death toll of the Yuuzhan Vong War was 365 trillion people. Their invasion path occupies less than a quarter of the galaxy, in most cases they don't make an effort to actually wipe out the defenders, and the Republic isn't actually that big for a galactic society: Coruscant has a trillion people, but planets like Corellia have a much more Earth-like population density, and given the prominence of each one there can't be that many worlds this size.
The official galactic population number is circa 100 quadrillion people. So the stated casualties make up 0.365 % of the total census population — Roughly the same proportions as the losses America suffered in World War II.
Some of this is the result of the Star Wars Expanded Universe having an extremely inconsistent portrayal of its basic scale. The movies give numbers in the range of "tens of thousands of worlds", including a lot of marginally developed worlds, while some EU sources bump this up to "millions of worlds" with a lot more development. Somewhere along the line, the math is bound to not add up.
Coruscant is described as one big city, with a population of one trillion. A population of one trillion spread evenly across a planet would have an average population density of only a few thousand people per square kilometer, and yet we see huge, sprawling, skycraper-laden areas that are almost completely full of people (Manhattan has a population density in the tens of thousands per square kilometer, now imagine multiple layers of that) . However, this isn't necessarily a contradiction because population density isn't uniform across the entire planet. There are marginally inhabited factory areas (like what Dooku flew over) and landing zones (like what Anakin crashed into), and the hugely populated parts in the movies are in the same general area, so it may simply be the (or simply a) "downtown" sector of the planet.
The novel Death Star makes a reference to several characters living in the "Southern Underground", which feels (in context) like a good-sized urban neighborhood, but is implied to be a much larger area. This doesn't make a lot of sense.
Much has to do with an utter lack of consistency and They Just Didn't Care among the writers. In the Black Fleet Crisis trilogy, Kube-MacDowell separated Coruscant into two individual continents separated by an ocean because he felt like it, despite knowing he was contradicting earlier novels.
The Armored Core series is a serial offender here, all the stats (armour strength, speed, weight, weaponry hitting power, generator capacity, lock on range, radar scanning speed and area, etc) are measured in numbers, with absolutely no indication of what unit of measurement is being used for any of them (except temperature and speed during gameplay, which are measured in Degrees.C and km/h respectively).
MechWarrior 4 has a heat gauge that measures your reactor's temperature in hundreds of degrees Kelvin. This wouldn't be such a big deal (it can range up to about 1400 degrees, a substantial but by no means unreasonable temperature swing) if it didn't start at zero. In the Kelvin scale, zero means absolute zero, the coldest temperature possible. However, MechWarriorLiving Legends seems to use the ambient temperature of the mech itself as the heat gauge - not the reactor's temperature. If you're in a lava environment, the heat gauge hovers at 300+ degrees Celsius, whereas an arctic environment has the gauge hovering at -20 Celsius.
StarCraft: When the Terrans first arrived to the Koprulu sector, they only numbered approximately 32,000. According to Blizzard's website, there are at least twelve billion Terrans in the Koprulu sector at the beginning of Starcraft II, and Raynor mentions Kerrigan killing eight billion people during the first game. He might have been including the Protoss but that still means you're looking at more than twelve billion humans living in the sector. As mentioned here, to have this many people after only 240 years would require the population to at least double every decade, for 24 decades, not taking into account the deaths that occur from any number of natural and unnatural causes, because the Terrans have a history of civil wars.
Zurg: Give them... a hundred evil! No, wait, a thousand evil! No, make it a MILLION evil! MWAHAHAHAHAHAHA! Grub: Gee, that's awfuly daring, your evilness, seeing as you only have an Evilness rating of 13. Zurg: Oh. Well, um, on second thought, how about we just give them a twelve.
There was also the whole episode which consisted of Zurg and the Rangers building bigger and bigger mechs. "And you're sure there is nothing bigger than grande?" "Meet my Vente range bot!"
A truly absurd example happens in Samurai Jack. The bounty that Aku places on Jack's head is a "googolplex" of whatever currency he uses. Actually paying such a bounty would be impossible, no matter what the value is of that standard of currency. A "googolplex" is a number used to express metaphysical ideas, and is described as a one with a "googol" of zeros after it. First of all, a "googol" is a one with a hundred zeros after it, and even that number is so large that nothing exists in such a quantity. Even if all the atoms of every molecule in the universe were counted, it wouldn't equal a googol. As for a googolplex, simply writing out such a number would require more space than the universe has available and more time than its age. So it is safe to say that no-one, not even Aku, could have that much money and that the idea of such a bounty is absurd.
Considering Aku, this might have been intentional on his part, in which case the ones with No Sense of Units would be the bounty hunters after Jack's head. (Or they're just plain stupid.)