The Scale of Large Numbers (and salt)

What do you think of when you think of a million? How about a billion? What picture pops into your head when someone complains about the US National Debt being over $9 trillion? How can a person even wrap their head around numbers that big?

I can't. And it got me thinking about how I could go about forming a better perspective for these mathematical concepts. The idea I came up with was to put the numbers into a smaller scale that I could more easily visualize. So I started counting grains of salt.

Sound boring? Oh, it was, I assure you. But I found the results to be very helpful, and surprising:

1 Hundred grains of salt is about how many come out of a salt shaker if you shake it once (if the shaker in question is not very generous). It's a very small pile.

1 Thousand grains of salt is about how many you get if you take a really generous pinch of salt. This is still a pretty unimpressive pile as piles of salt go.

1 Million grains of salt is slightly less than what fits in a 1/2 cup measuring cup. Still not a whole lot, but quite a bit bigger than 1,000.

1 Billion grains of salt is equal to 25 gallons. If you can picture a 50 gallon drum filled half way with salt, that's about a billion grains. That's a lot more than the million that fit in the 1/2 cup!

1 Trillion grains of salt is equal to 25,000 gallons, or 3,342 cubic feet. That will completely fill a 21x20x8 foot room, roughly the size of a small classroom or a large living room. That is a lot bigger than that half of a drum that the billion fit into, and a whole lot bigger than the 1/2 cup that the million grains fit into. At that rate, would you even notice if a few million were added or subtracted?

1 Quadrillion grains of salt is equal to 25 million gallons, or roughly 3.3 million cubic feet. If you took a football field, including the end zones, and piled salt onto it, all the way to the edges, 60 feet deep, you would have roughly one quadrillion grains of salt! Or, if that's a little hard to visualize, imagine 10 football fields all covered 6 feet deep with salt... The perspective kind of breaks down again, doesn't it? (Author's note: Please don't try this at home; the grass on those football fields will never grow back again.)

Not wanting to wax political here, but thinking back to the question about the national debt being roughly $9 trillion... In salt-grain terms, that's 9 small classrooms filled with salt. Except each grain costs $1. The US Population is about 304 million, which means that each person in the US would have to pay roughly $30,000 to pay it off.

But before you get too worked up about the $30,000 you owe, realize that it only represents about a half of a teaspoon of salt. And that's barely enough to make cookies with.

[Postscript: My good friend Taylor gave me the idea to do this same exercise using seconds. Here are the results using lengths of time!]


You can check my math and my methodology here at this Google Spreadsheet.