Giggety giggety gigapennies

By Phil Plait | January 12, 2009 2:30 pm

So how well do you grok big numbers?

I’m an astronomer, so I do OK. More importantly, I am a huge geek (bordering on dork) when it comes to numbers, and when I was a kid I would sit and memorize the names of the big exponents: decillion, nonillion, octillion (my favorite; I like the way it sounds).

But what do they really mean? How big are these numbers? Most of us have a hard time grasping anything past about 16, so a million is hard. The bailout is in the hundreds of billions of dollars, and the national debt in the trillions. How much cash is that?

One million pennies.

Turns out, it’s a lot. But it’s hard to grasp, so you might want to take a look at a site called Megapenny. It’s pretty cool, using simple but effective graphics, stepping you through stacks of pennies to represent big numbers. I was doing OK up to about a billion pennies, but then at 10 billion I started to freak out a little bit.

A billion is a big number.

And now maybe you’ll have an idea of just how big. You see that picture? That’s only a million pennies (plus change… literally). That’s only ten grand’s worth. Think you know how many a billion is? Guess first, then click through. You may be surprised.

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Comments (79)

  1. IVAN3MAN

    Q: How many Phil Plait clones does it take to change a light bulb?

    A: A “bazillion”!

  2. Yeah, too bad the 70,000,000,000,000 (70 trillion) pennies the US government gave the banks all went to nothing, completely unregulated. Grrrr!!!

  3. …octillion (my favorite…)

    The mollusk-huggers will love to hear that.

  4. IVAN3MAN

    Phil Plait: “That’s only ten grand’s worth.”

    Er… I think that should be collective singular: That’s only ten grands’ worth.

  5. Vernon Balbert

    Wow, 1 quintillion pennies make a Borg cube!

  6. FYI, Kokogiak media also gave us this:

    http://kokogiak.com/solarsystembodieslargerthan200miles.html

    …Which I probably first saw through this blog.

  7. I remember how a group of special forces going into Afghanistan talked about how they took millions of dollars with them in cash. They filled several large boxes, the author whose names eludes me at the moment commented on how that amount of money doesn’t fit into a briefcase like in the movies.

  8. Radwaste

    Hey – don’t even start to think that very large integers are tough. Those, from 1 to infinity, are at least denumerable. There are entire classes of mathematical concepts that are not, such as pi. Yes, no matter how big a number you come up with, pi has more digits than that.

  9. Alan French

    Cool. Perhaps helpful in picturing out national debt of 10.6 trillion dollars.

    Big numbers in science are fun. Big numbers in the national debt are not.

    Clear skies, Alan

  10. stopgap

    “The bailout is in the hundreds of billions of dollars”

    This is technically incorrect. Bloomberg has the figure pegged around 8.5 trillion available and just over 4 trillion already used. Now the 750 billion figure is what the executive branch has on hand to “help” the economy. When you factor in the Federal Reserve the number is much higher than the 750 billion the mainstream media keeps repeating like mindless drones.

    http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2008/11/26/MNVN14C8QR.DTL

  11. I see no pennies. Those are cents. Pennies are British.

    Pedantry aside, what does Graham’s number of cents look like? Even looking at finite numbers astronomers and physicists are just scratching the surface.

  12. IVAN3MAN

    Phil Plait: “I was doing OK up to about a billion pennies, but then at 10 billion I started to freak out a little bit.”

    Young-Earth creationists seem to freak out about any number above 6,000!

  13. Radwaste: the number of digits in the decimal expansion of $pi$ is still denumerably infinite.

  14. Davidlpf

    That is a penny for every 1 in 3 americans.

    @Ivan3man
    the youngearth creationists numbering system restarts at 6000 like the Mayan calendar.

  15. fracai

    Only in North America and the general scientific community is this number (1,000,000,000) called a “billion”.

    Hah, yeah. Only those 2 small groups.

  16. Miranda

    After the US financial bailout, when I was trying to explain the size of big numbers to my coworkers (yes, coworkers), I used seconds:

    1 million seconds is about 11 days
    1 billion seconds is about 31 years
    1 trillion seconds is about 31,000 years, or about the time Neanderthal man disappeared from the earth.

    However, I have to say, I like the visual representation of the pennies!

  17. rm

    @John Armstrong: Graham’s number is so big you can’t even write it down without inventing a special notation for it. You could fill the entire observable universe with pennies (about 3e+80 cubic meters according to wikipedia) and not make a scratch in it.

  18. Santoki

    I like the idea of visualizing numbers to help understand them. But expressing dollar amounts in pennies just creates bigger numbers.

    Am I wrong?

  19. gopher65

    We’ve been having a related argument on and off on Wikipedia for years. How do you display big numbers (such as in the “Universe” article) in such a way that people can understand them? Some people want to use kilometres, arguing that light-years is a nonsensical unit for most people. But I argue two things: 1)most people understand neither scientific notation nor prefixes like exa- and yotta-, so that makes kilometres useless, and 2)even if that weren’t true, saying something like “This star is 107 trillion kilometres away” conveys absolutely nothing except, “wow, that’s a big number”. Plus the whole long/short scale issue. Bah, humbug.

    And really, we can do that with light-years just as easily as with kilometres. The *real* problem is that there is simply no way to convey distances that large, because humans simply *cannot comprehend* such big numbers. We get a buffer overflow error, then we simply convert units.

    “150 million kilometres?” *WARNING: buffer overflow; downsize units* “Oh yeah, that’s only 1 AU.” We really do not seem to be able to understand numbers bigger than a few thousand.

  20. Davidlpf

    Ironically lightyears are not used much in astronomy the unit of choice is the parsec, lightyear is often used to explain things to the general public.

  21. Alan French

    I was equating 10 trillion pennies (cents) with10 trillion dollars as a key to understanding the number. No need to complicate things by going for equivalent amounts of money!

    Clear skies, Alan

  22. After looking at that last cube, I have a terrible fear that resistance is futile and I will be assimilated…

  23. Turing E.

    Psh. Astronomers don’t grok really large numbers. Astronomers grok pretty big numbers. Let me know when an astronomer has to use Graham’s Number for anything.

  24. becky'sthoughts

    Thanks for the link. I’m always looking for new ways to teach my Girl Scouts about money. Great site.

  25. JB of Brisbane

    I am reminded of a joke: George Dubya asks his information officer about the latest news from Iraq. The info officer replies, “Mister President, we’ve had a report that two Brazilian soldiers were killed today in Tikrit”.

    “My god, that’s terrible!” says GWB, then after a short pause – “How many is a brazillion?”

  26. when I was a kid I would sit and memorize the names of the big exponents: decillion, nonillion, octillion

    Whew, I thought I was the only one who did that. I also once filled several notebooks with Roman numerals just to see how high I could go. Thanks for the link, that’s a neat way to visualize increasing orders of magnitude.

  27. I have a different way of visualizing a billion.

    Most people have a feel for a millimeter. It’s about the size of a BB (the kind that are shot out of a Red Ryder lever action range model carbine with a compass in the stock and this thing that tells time).

    Lay down a meter stick and that’s 1,000 mm or 1,000 BB’s in a row. Extend a layer of them one meter deep and that’s one million. It’s a lot of little spheres, but something you can visualize. Now just stack up 1,000 layers of those and you have one billion BB’s, enough to keep Ralphie in ammunition for at least a week.

    A one-meter cube is something that is intuitively understandable, as is a single BB. Most people can make some sort of connection between them.

    – Jack

  28. bjn

    Very cool. Like the Nehru jacket.

    Looking at all that copper, it’s way past time to do away with the penny (or cent if you must).

    http://www.retirethepenny.org/

    Not only are pennies a waste of money and time, they’re a waste of resources. With that huge block of actual minted coins in mind, magine the energy and impact on the enviroment from mining the zinc core material and copper plating, refining it, minting the coins, and transporting them through the aforementioned processes and through their usable lifetime.

  29. Jack Mitcham

    One of my favorite big-number problems is the number of possible arrangements of a deck of cards. 52! comes out to be a huge number. So huge, that if you shuffle a deck of cards, it’s very probable that that particular arrangement has never occurred before in the history of the world, and will probably never occur again.

    If you gave every human who ever lived a deck of cards, and they shuffled it every second of their lives, never stopping to eat, sleep or anything… Just shuffling cards, they would only come up with a tiny fraction of the possible combinations, even if they were guaranteed to never repeat an arrangement.

  30. Radwaste

    @ John Armstrong

    The History of Pi calls pi non-denumerable because, unrelated to my implication that it has an infinite number of decimal positions to express it, the value at each position does not “count upwards” as any expression of an integer.

    Please do not assume expertise on my part. I note only some exceptions to popular concepts.

    —–

    Those of you talking about “debt” might step back a minute and realize how little that means to the consumer, for whom possession is 10/10ths of the economy. Also, it would be instructive to consider the definition of the dollar.

  31. Kokogiak is also the editor of The Big Picture at the Boston.com.
    Talented fellow!

  32. Randy Griffin

    @Jack Hagerty – a BB is 4.5 mm, I believe. Usually express as .177 caliber in the U.S.

    And, by the way, I would completely disagree that most people have a feel for a millimeter, at least in the U.S. Or a meter, either.

    I’ve worked with people that, given a drawing with dimensions in millimeters and (digital!) metric gauges to measure with, will still convert the measurements to inches. I really don’t understand why they just can’t compare two numbers regardless of the units.

  33. Russ

    The natural question then is, how many pennies must be contained in a penny cube until it becomes a black hole?

  34. Colin J

    Ummm… Phil – “Bordering on dork?” Yeah, bordering…. :)

  35. Russ, with a little as the mass of one penny if it is used to create a mini black hole in the LHC. On the other end of the scale I think the number you are looking for is a frackzillion. :-)

  36. gopher65

    Davidlpf:

    Yeah, that was something that came up in our discussions. But really, who outside of astronomy has any idea of what a parsec is? Ultimately it was decided that beginner articles like “Universe” are… well… beginner articles;o). So they should use the units (and language) that is most commonly understood by the public in the field in question.

  37. Russ

    I’m specifically talking about normally stacked pennies, not pennies crushed by some massive galactic collider.

    I’m guessing it’d be somewhere in the range of enough pennies to fill out earths orbit spherically.

  38. Tom

    Personally I find the fact the size of the one quintillion block of pennies even more disconcerting when I consider that it is still several orders of magnitudes less pennies than the estimated number of stars!

  39. j-o-h-n

    The minimum mass for a black hole is 4.5e25g, a penny (new) is 2.5g, so you would need about 1.8e25 pennies to fashion a black hole.

  40. Tim G

    A baker’s trillion is 10^13.

  41. Tim G

    That’s our National Debt, a baker’s trillion dollars.

  42. Rowan Bulpit

    Tim G: I don’t know why I found that so funny, but I just laughed hard for a full minute.

    Great visualisation, some of those large numbers just freaked me out (in the best way possible).

  43. Eddie Janssen

    I once made a ‘book’ with 1 million dots. 264 pages (A4, one inch to each side, Times New Roman 12). I showed it to 10-12 years. IIRC the reason was to explain how big the sun was. One million earths in one sun.
    The number of dots gets quite overwhelming when you are paging through the ‘book’.

  44. Thomas Siefert

    I learned of big numbers through a joke:

    If you are rich and don’t like your wife’s company, give her a million dollars and send her shopping with an allowance of $3000 a day. You wont see her again until about a year later.
    Give her a billion dollars and you wont see her for about 900 years.

  45. k9_kaos

    I’m surprised nobody’s mentioned MegaMoo yet!

    “Yes we’re dealing with cows now, and not pennies. Why? Well, why not?”

  46. PG

    Yay, semantics!

    @IVAN3MAN: Actually, you wouldn’t call $10,000 “ten grands” would you? You’d call it “ten grand”. It’s one of those words that looks singular, but is plural, like “sheep”.

  47. Thanks for the update, Randy.

    OK, so a BB is 4.5 times bigger than my thought experiment standard. How about #12 bird shot? That’s 1.3 mm. (I always thought that “BB” shot was called that because it was in between buck shot and bird shot in size).

    As for the “most people” I was referring to, I meant elementary and middle school students that I teach rocketry classes to. They haven’t had a lifetime of the English system to unlearn and usually have a feel for millimeters and meters since they’re right there on the rulers in class.

    – Jack

  48. Mike

    How big is 10^92 pennies? ^.^

  49. bassmanpete

    Eee, when I were a lad back in’t ’50s, a million pounds, or even US dollars, was a lot of money and billion was very rarely heard. Now a billion is as common as muck and trillion is becoming quite commonplace. Any guesses as to when quadrillion will creep into the language of finance? Or will there be a revaluation so that one pound/dollar becomes the equivalent of 100 of todays units?

  50. IVAN3MAN

    @ PG,

    Initially, I did have some doubts about that before posting my comment above, but when I ran a check with Google Spell-Check for “grand’s”, it highlighted the word in red (like it did just now before posting this) and suggested “grands”, so I went with that.

    However, now that you have mentioned it, I have checked with the Oxford English Dictionary, and you’re right: “grand” as in “a thousand dollars/pounds” is already plural, like “people” or, as you said, “sheep”.

    Also, Microsoft Works Word Processor concurs with the O.E.D.

    So, my apologies to you, Dr. Phil Plait, I was in error.

    Note to self: Don’t trust Google’s bloody spell-checker!

  51. To be honest I was actually expecting the billions of pennies to be larger but I suppose I’m kinda used to the European 1,000,000,000,000 definition of a billion. Wonder what they’d look like stacked up in a single pile though – skinny space elevator anyone?

  52. Jean-Denis

    From the Megapenny project web site: “All weights and measurements are U.S. standards, not metric”.

    What a pity.

    Most of the world won’t be able to use the web site without mentally converting to common units such as kg and m.

  53. Didac

    There are two reasons to use very big numbers:
    – 1) A huge collection of things (say, the number of hydrogen atoms in the universe).
    – 2) The improper use of a very tiny unit of measurement.

    This 2) is the problem with trying to use $ to measure macroeconomical phenomena. It’s like to measure yourself in micrometers or in nanograms. Or to measure the Sun in foots and pounds.

  54. Cool site! Some comments:

    I wish they had gone higher. I wanted to see the Earth, or perhaps even the Milky Way galaxy dwarfed by pennies. That would have been very cool.

    I think they should add exponential notation to the pages, i.e. powers of 10. Let’s encourage people to understand science literature better – I know it’s only a small step, but every little helps.

    In my experience as a Brit, the British “billion” is all but dead. Most people here now use the U.S. one – probably because the most common place they hear the word is on TV when financial matters are discussed, and these are often global issues so it would not make sense to mix the two. Looks like you win this time, America!

    Actually, I think 1,000,000 should have been a billion because “bi” implies two, and there are two groups of triple zeros. Still, we’re stuck with having to subtract one and multiply by three now (e.g. quintillion sounds like 5, so 3 x (5 – 1) = 12, therefore it is 10 ^ 12) so we have to get used to it. I think the same thing about intervals in music. An octave? Nonsense! There are seven steps, not counting the first note which is zero, therefore it should be a heptive. Which would be hep, man.

  55. Michelle

    I have so many pennies in my room. They loiter all around – in my bank, on my floor, and sometimes when I wake up in the morning there’s one stuck to my buttcheek. I’m always too lazy to use them.

    So you can imagine how I’d feel if I had a quintillion of it. I’d go insane!

  56. Gordon

    “sexvigintillion”
    My new favorite word.

  57. gopher65

    Quintillion is not 10^12.

    In short scale:

    Billion = 10^9
    Trillion = 10^12
    Quadrillion = 10^15
    Quintillion = 10^18

    So 1 Quintillion metres would be 1 exametre, assuming that I’m remembering my prefixes correctly.

    I believe that if you are looking a groups of zeroes, it goes: (# of groups)*3 = exponent.

  58. Andrew

    The MegaPenny site reminds me of the Powers of Ten film, which I remember seeing several times at school. Makes you feel so, sort of, insignificant, doesn’t it? But surely the method is to *add* one and multiply by three – a million is (1+1)*3 = 6 zeroes; a billion is (2+1)*3 = 9 zeros; etc. A quintillion is 10^18.

    The Japanese and Chinese number systems use multiples of the myriad (10^4) rather than a thousand; in India, they tend to use the lakh (10^5) and crore (10^7).

    The usual Western musical notations use a heptatonic scale, with eight notes and seven intervals. I don’t know about you, but I tend to count things “one two three four…” rather than “zero one two three…”.

  59. Wow, they even mentioned the milliard! *Dances a litte dance.*

  60. Mister Rose

    Black hole penny?

    (please forgive my math errors. I am trying to do this using Windows Calc program).

    We’ll start with 10 megapennies, since that has some convenient measurements.

    10 Mp = 10,017,024 x 0.00283495231 kilograms / penny = 28427 kg = 6.116 m^3

    Minimum stellar mass black hole ~ 1.5 solar masses = 3×10^30 kg

    3×10^30kg / 28427kg = 105,533,471,699,440,672,599,992,964 = 1.055 x10^26 Mp = $1.055 x10^24

    1.055 x10^26 Mp occupies about 645,442,712,913,779,153,621,556,970 cubic meters or

    645,442,712,913,779,153 km^3 = 6.45 x10^17 km^3

    V = 4/3 pi R^3 -> R = cuberoot( 645,442,712,913,779,153 km^3 * 3 / (4*pi) )

    R = 536113 km.

    That’s about 500 Jupiters or so?

  61. My favorite big-number rule of thumb uses time:

    * Million seconds = 12 days
    * Billion seconds = 32 years
    * Trillian seconds = 32,000 years

    This really drives home the vast difference among those similar-sounding numbers: Going from a million to a billion is like going from a fortnight to a generation; from a billion to a trillion is going from one generation to before the last Ice Age.

  62. … except that I usually spell “trillion” correctly

  63. JoeSmithCA

    Graham’s Number in pennies. Scale that against the universe I imagine.

  64. Octillion is a cool number. :)
    If I remember rightly, the Sun is roughly 2 Octillion tonnes in mass…

  65. Russ

    J-o-h-n and Mister Rose, you aren’t doing the black hole calculation right. There is no minimum black hole size. The only thing that matters is the amount of matter contained in a certain amount of space. So from the scharzchild radius equation, it must be possible to derive the minimum radius or mass for matter of a particular density to form a black hole.

  66. It surprises me that a site that (sort of) promotes science uses a term like “35 times less”. I see this kind of terminoligy used more and more, although it really doesn’t mean anything (least of all 1/35)

    It’s definitely cool to get that kind of visual representation though

  67. And yes, I realise I spelled “terminology” wrong.

  68. Jim Baerg

    Hey k9_chaos: Regarding MegaMoo

    You do realize that if they went up to 10^12 male cattle that would be terabull.

  69. Lars Says: “Wow, they even mentioned the milliard! *Dances a litte dance.*”

    Wasn’t he the 13th president?

    – Jack

  70. Gary Ansorge

    Visualizing big numbers of things tends to top out at around,,,7 items,,,Go ahead, try visualizing the bricks in a fence.

    For really BIG numbers, try the subtend route, as in 10 subtend 4, which means 10^10^10^10^10,,,by the time you get to the second calc, the exponents are too big to write down.

    Gerard O’Neille calculated that there were about 3000 planet Earths worth of resources in the moons and asteroids of our solar system. It took about 10,000 years from the development of agriculture to the present for humans to settle and use the resources of the entire planet Earth., so 10,000 times 3000 planet Earths would take about 30 million years,,er,,,of course, that’s just a linear progression and as we all know, humans like to increase exponentially,,,but that gives a small idea just how big our solar system is and we have a whole universe gazillions of times bigger to explore,,,I’m really looking forward(WAY forward) to seeing that,,,(Whatdayoumean I don’t get to live that long??? Hmph. Snarky pessimist!)

    GAry 7

  71. SteveG

    Big numbers can be hard to comprehend.

    However, big numbers also multiply small errors.

    According to the US Mint, a penny is 1.55 mm thick (the metric system for US coins, go figure). But that makes a penny .061023 inches tall, just less than .0625, 1/16th of an inch. So 16 pennies are .976 inches tall, not 1 inch. 40 pennies are 2.44 inches tall, not quite 2.5. By the time you get to a cubic foot of pennies, you’re off by a quarter of an inch.

    I’m not one to pick on details – or maybe I am. But I was impressed when I thought a penny was 1/16th of a foot wide and 1/16th of an inch tall. I thought, how elegant! I wondered if it was by coincidence or design. When I checked then I realized it wasn’t quite so.

    Still a great site, though I might suggest a few qualifiers in the statements such “almost a foot tall”, etc.

    Just my 2 cents…

  72. SteveG

    Interesting table on the names of numbers. I don’t know how accurate it is truly but it seems to make scents (I couldn’t resist)

    http://www.jimloy.com/math/billion.htm

  73. Andrew R

    interesting to note…one quintillion pennies stacked = a little over 1/6 of a light year long

  74. lars bruchmann

    I heard a penny costs over a penny to make, we should just get rid of them. then this entire string would be irrelevant, right? lol. that borg cube of pennies was terrifying though! so if i don’t have a penny, will a half penny do?

  75. Nancy B.

    I can’t wait to show this to my 5th graders, who freaked out when we read that the sun will die out in a few billion years. This should help with their visualization of numbers.

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