The Big and Small of Scientific Numbers
Ask Science 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
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The Big and Small of Scientific Numbers
Sometimes in science, we talk about things that are either really big or really small. So today, I want to take a look at some of the numbers that are frequently thrown around, and give them a bit of everyday perspective..
Faster than a Speeding Bullet
Faster than a Speeding BulletFirst, let’s take a look at some common scales of speed. Let’s imagine that you have a very fancy car that can travel at insane speeds, without any ill effects. Normally, on an interstate you can drive about 70 miles per hour. Let’s imagine that you live exactly 70 miles from your favorite movie theater. How long before the show starts would you have to leave your house in order to arrive just in time?
Ignoring the time it takes you to get in and out of the car, and assuming that you could drive the same speed the entire time, at a speed of 70 miles per hour it would take you one hour to get to the theater. That was probably pretty obvious, but let’s take a look at some other speeds.
Let’s imagine that you could drive your car at the speed of sound. That hour-long trip would only take you about six minutes at the speed of sound. Of course, the speed of sound can vary somewhat depending on temperature and atmospheric pressure, but we’ll ignore that for now.
Six minutes is great, but what if you’re a really big procrastinator? Fortunately, your car can also travel at the speed of light, so how much time would it take you to get to the theater going at the speed of light? I hope you’ve buckled your seatbelt, because at the speed of light it would take you just 6 millionths of a second.
That sounds pretty fast, right? But just how small is a millionth of something?
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.
Population
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.
Conclusion
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.
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Photos of swirling numbers and tiny house in hands courtesy of Shutterstock.
