The Big and Small of Scientific Numbers

Everyday Einstein takes a look at some of the very large and very small numbers frequently thrown around in science, and helps makes them easier to visualize.

Lee Falin, PhD
3-minute read
Episode #109

It’s a Small World

To understand millionths, let’s imagine that you live in a house that is about 12 feet in height, from the yard to the tip of the roof. Now let’s pretend that you have an exceptionally powerful and mean-spirited wizard living next door, who decides to play pranks on his neighbors by periodically shrinking their houses.

One day, you come home and find that your house is only a tenth of it’s previous size. That would mean that your house is now only a little over a foot tall--pretty cramped living conditions! The wizard isn’t done yet, though: just to show off a bit, he uses his magic to shrink a local 10-story office building down to a hundredth of its size, which makes it also a foot high.

Fortunately, the homeowner’s association acts and forces the wizard to move out. He relocates to the city, and is soon back to his old tricks. This time, though, he applies his magic to a local football stadium, shrinking it down to a thousandth of its size--which allows the entire stadium, seats and all, to fit into his living room.

For his final trick, he decides he’d quite like his own airport, as well. So he shrinks JFK airport down to one millionth of its former size of 4930 acres, making it small enough to fit into his master bathroom.


The world has around 7 billion people living on it, so how many people is that? One way to think about that number of people is to consider that New York City has a population density of about 26,000 people per square mile. That means if you were to draw a square over a map of New York City that was one mile long on each side, there’d be about 26,000 people in that square.

Now the state of Texas has a total area of about 269,000 square miles. So if you were to take all of the people in the world and cram them into Texas, the entire state would be as crowded as New York City.

Although this would cause quite a strain on the Texas road system, it would also leave the entire rest of the planet completely uninhabited. Which shows just how little of the Earth’s surface humans currently use.


Hopefully, today’s episode helped you get sense of scale for some of the very fast, very small, and very large numbers you hear being used in science.

If you liked today’s episode, you can become a fan of Everyday Einstein on Facebook or follow me on Twitter, where I’m @QDTeinstein. If you have a question that you’d like to see on a future episode, send me an email at everydayeinstein@quickanddirtytips.com.

Photos of swirling numbers and tiny house in hands courtesy of Shutterstock.


About the Author

Lee Falin, PhD

Dr. Lee Falin earned a B.S. in Computer Science from the University of Illinois, then went on to obtain a Ph.D. in Genetics, Bioinformatics, and Computational Biology from Virginia Tech. 

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