How to Think About Astronomically Large Numbers

How big is the number 1 million? 1 billion? Or 1 million billion? How can you think about these and even larger numbers so that you actually comprehend their immense sizes? Keep on reading to find out!

Jason Marshall, PhD
4-minute read
Episode #203

Money StackIf you're like most people, you find really big numbers really hard to comprehend. Sure, it's clear that millions, billions, or trillions of something are an awful lot of whatever that something is, but getting a firm grasp around just what that means is no easy task.

But there are ways to make sense of these astronomically large numbers and build an intuition for just how big they really are. What's the best way to do it?

That's exactly what we'll be talking about today.


How to Think About Millions

In my opinion, the best way to develop intuition for large numbers is to come up with simple visualizations that help put things in perspective. One common way to do this is to think about stacks of paper money. A typical $1 bill has a thickness of about 0.004 inches—which is also the approximate thickness of a normal sheet of printer paper.

If we stack 1,000 dollar bills, we'll have a pile of money that's about 1,000 x 0.004 inches = 4 inches high. Let's use this as our reference point to think about just how large the number 1,000,000 is. Namely, $1,000,000 worth of $1 bills would make a stack of money about 1,000,000 x 0.004 inches = 4,000 inches high. Which turns out to be just a little more than the length of a football field!

1,000,000 is to 1,000 as the length of a football field is to the thickness of a sheet of paper.

So 1,000,000 is to 1,000 as the length of a football field is to the approximate length of a credit card. And 1,000,000 is to 1 as the length of a football field is to the thickness of a sheet of paper. Which, for me at least, is a much more tangible way to think about what "millions" really means.

How to Think About Billions

How about billions? If we play the same game with stacks of dollar bills we find that one billion $1 bills makes a pile of money that's 1,000,000,000 x 0.004 inches = 4,000,000 inches high. How high is that? Pretty high—about 60 miles. For comparison, that's approximately the thickness of the Earth's atmosphere! Which means that 1,000,000,000 is to 1,000,000 as the thickness of Earth's atmosphere is to the length of a football field.

But let's not just play this dollar bill game, let's come up with another visualization that you can use to think about the magnitudes of these numbers. In particular, let's think about time. How long is one billion seconds? It's just under 32 years! Or, to stick with our "astronomical" theme, it's about the same amount of time that Saturn takes to complete one orbit around the Sun.

For comparison, one million seconds is about a measly 11.5 days and one thousand seconds is about 16.5 minutes. No matter what comparison you use, the difference between thousands, millions, and billions is huge!


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.