Large Number Place Value

How Low Big Can You Go

It's fairly difficult to escape knowing large numbers into the millions, billions, and trillions, for a few reasons. First and foremost, the amount of people and money in the world only wanders into the billions and trillions, respectively (so far at least!). As such, we're often hearing these figures routinely in every day conversations and in the news. And if we're going to be familiar with trillions and billions, we're probably going to have familiarity with millions and thousands, if not for similar reasons than for the fact that we learn them in school.What's on the other side though? Even though it will be a while before the global count of either people or money will require us to know what comes after trillions, single-device computer storages are currently fast approaching that threshold.One trillion is represented numerically as a $1$ with twelve zeroes following it (13 place values in all). There are precious few reasons to practically work with numbers that exceed 33 place values, and many students I encounter have been taught the names up to that point once or twice, though it's the kind of thing you forget the next day.Here are the "common" large place values for numbers with "even" three groups of zeroes.

ThousandThree Zeroes ($10^3$)You are utterly familiar with thousands for..... well thousands of reasons!

MillionSix Zeroes ($10^6$)It would take most people somewhere around $23$ days to count to a million (at a "normal" pace).

BillionNine Zeroes ($10^9$)About 3.5 months before your 32nd birthday, you will have been alive for one billion seconds.

TrillionTwelve Zeroes ($10^{12}$)According to everyone's favorite free encyclopedia, the United States federal 2016 fiscal year budget (how much the government spends in a year) is estimated to actualize at about $3,854,000,000,000$. That's a lot of cheddar.

QuadrillionFifteen Zeroes ($10^{15}$)Scientists believe (as of 2017 anyway) that the universe was created by the Big Bang approximately $13.7$ billion years ago, which is about $43$ quadrillion seconds.

QuintillionEighteen Zeroes ($10^{18}$)In the span of a quintillion years, our sun's lifespan that we are smack in the midst of right now (birth to eventual death) could have happened $219,000,000$ times.

SextillionTwenty-One Zeroes ($10^{21}$)In the existence of humanity, it is certain that humans collectively have not yet uttered one sextillion words (and will not have for thousands of years at our current population size).

SeptillionTwenty-Four Zeroes ($10^{24}$)This many gallons of water could fill the Great Lakes about $167,000,000$ times. This is so large it's really incomprehensible, but scientists believe that there are somewhere around $7$ or $10$ septillion stars in the known universe.

OctillionTwenty-Seven Zeroes ($10^{27}$)One billion billion billion - quite a size. Going the other way on the size scale, to demonstrate how small an atom is, you have somewhere around 7 octillion atoms in your body.

NonillionThirty Zeroes ($10^{30}$)I'm sure by now all of these comparisons sound the same, but about $259$ Nonillion atoms of water go over Niagara Falls each second. That's $681,750$ gallons per second, which can fill about $1$ olympic sized pool.

DecillionThirty-Three Zeroes ($10^{33}$)Our sun weighs approximately $2$ decillion grams.

Well then! Why stop at decillion? In my travels I find that decillion is often the largest named number students are taught, probably first because there are few reasons to ever quantify something larger, and second because it is a nice stopping place, being the one that hits the prefix that uses $10$, and prefixes for $11$ and up are generally uncommon and awkward.

What's After That?

There are some truly bored people out there, to have come up with names for numbers beyond a decillion. The naming convention follows the Latin prefixes you might expect, but there's hardly a point to knowing these, in any situation beside googling this out of boredom. My practical definition of "the largest number" is the number of atoms in the universe, which scientists approximate to be about $10^{80}$ more or less. Therefore I don't even see why we bother knowing or naming a googol ($10^{100}$) (which is where its similarly named search engine gets its namesake from). Or a googolplex ($10^{\mathrm{googol}}$).In any case, the show you paid to see isn't my trying to convince you not to bother. The list is presented below. Try to see if you can spot the pattern and start predicting them as you read sequentially!Undecillion - $10^{36}$Duodecillion - $10^{39}$Tredecillion - $10^{42}$Quattuordecillion - $10^{45}$Quindecillion - $10^{48}$Sexdecillion - $10^{51}$Septendecillion - $10^{54}$Octodecillion - $10^{57}$Novemdecillion - $10^{60}$Vigintillion - $10^{63}$Unvigintillion - $10^{66}$Duovigintillion - $10^{69}$Trevigintillion - $10^{72}$Quattourvigintillion - $10^{75}$Quinvigintillion - $10^{78}$Sexvigintillion - $10^{81}$Septenvigintillion - $10^{84}$Octovigintillion - $10^{87}$Novemvigintillion - $10^{90}$Trigintillion - $10^{93}$Untrigintillion - $10^{96}$Duotrigintillion - $10^{99}$Googol (this is the one the search engine is named after!) - $10^{100}$Tretrigintillion - $10^{102}$Quattourtrigintillion - $10^{105}$Quintrigintillion - $10^{108}$Sextrigintillion - $10^{111}$Septentrigintillion - $10^{114}$Octotrigintillion - $10^{117}$Novemtrigintillion - $10^{120}$Quadragintillion - $10^{123}$And while by this point you can fill in the in-between blanks (could you guess that the next few are unquadragintillion, duoquadragintillion, and trequadragintillion?), here are a few more milestone numbers.Quinquagintillion - $10^{153}$Sexagintillion - $10^{183}$Septuagintillion - $10^{213}$Octogintillion - $10^{243}$Nonagintillion - $10^{273}$Centillion - $10^{303}$And that's about all I can find agreement on. For whatever point we can find to naming such quantities so large that they would encapsulate several decillion universes worth of mass 🙃
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