In the last few minutes of a session, I had a student hit me with this question, just out of the blue:
Does anyone have one googol dollars?
For those who aren’t familiar with “googol”, it’s actually not a misspelling of everyone’s favorite verbed search engine. It’s this very large number:
… or, with commas:
… because those commas, of course, make all the difference.
It’s probably for the better I wasn’t taking a sip of water when this question came up, since I almost did the dry version of the classic spit-take, but I caught myself in time, paused, and instead said, “… Ok, well, let’s have some fun with this.”
The average dollar bill weighs 1 gram. For ease of transport, dollar bills come in “straps”, or bundles of 100. We’re going to do ourselves a couple favors and say (1) that we’re only going to use $100 bills, to minimize the number of dollar bills we will have to create, and (2) the paper strips holding the straps magically have no mass. Sure, this is entirely wrong, but, trust me, we’re going to need all the mass we can have available for $100 bills.
According to the US Federal Reserve, there were 38.1 billion currency notes in circulation in 2015. While this doesn’t just mean dollar bills (it could include other valid notes of value), this provides us our first estimate: If we convert all of these notes up to $100… we’re nowhere close. That would give us $3.81 trillion, which gets us a paltry 3.81 x 10^-88 percent of the way there. In numbers?
This clearly won’t do, not if we’re trying to become the richest person ever known, and quite possibly in past, present, and future, at that. So, let’s do something mathemagical here.
Our home, good old Planet Earth, has a mass of 5.972 × 10^24 kg, or in grams like our money, 5.972 × 10^27 g. I’ll spare you writing out the big number, but that number, in grams, is also exatcly how many $100 bills we could have if we could turn every single atom of the Earth into $100 bills (this is where we put the “magic” in “mathemagical” – this would take ridiculous amounts of energy that we’re going to magically ignore the need for right now). By doing so, we get a grand total of $5.972 × 10^29. We also now lack for a place to store all of these $100 bills (one of the downsides of no longer having a planet), but I’m sure we can just grab a spare black hole for a wallet. Unfortunately, we need 70-and-a-half more zeroes, so we’re going to need some more mass…
… so we’re going to use the entire Solar System!
But it turns out this doesn’t actually help too much more. The Sun, all the planets, every moon, and all sorts of other objects like asteroids and comets and other items (oh my!) comes to a collective mass of 1.991 x 10^33 grams, or $1.991 x 10^35 dollars, and we’re still just under 65 zeroes too short. Can we go bigger?
Of course! Our Solar System isn’t just floating around in space. It sits on a far arm of the Milky Way galaxy, which has a mass of 1.153 x 10^45 grams. I’m going to guess now though, my savvy reader, that you’ve caught on to the pattern – the number of dollars is two more than the number on 10^##. At $1.153 x 10^47 dollars, we’re just under half the number of digits!
And this is where we reach the point of impossibility. Best estimates state that there are on the order of 100 billion galaxies, and even if we take all of these into account, we’re going to need some of that as-yet-undiscovered dark matter to get things to work – converting every single galaxy, with generous estimates, only gets us to approximately $1.153 x 10^58 dollars. To put this titanic number into perspective, compared to our $1 googol? Halfway to $1 googol would be $5 x 10^99.
At this point, it’s safe to say we’re not going to get $1 googol. If we somehow could get this to work though, we wouldn’t have a planet to put it on. We might be able, somehow, to arrange in space, but this much money just might make for the strangest galaxy of them all…
About the Author: Jason Orens – a Math and Computer Science Instructor, has been tutoring with Oxford Tutoring for over nine years. Utilizing the student’s existing knowledge and a touch of humor, Jason strives to remove students mental barriers between themselves and the difficult, technical materials. He combines his years of tutoring experience and expertise in the fields of Math and Computer Science to give his students the tools they need to succeed in these challenging classes.