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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!

By
Jason Marshall, PhD,
June 20, 2014
Episode #203

Page 2 of 2

How to Think About Trillions

Continuing up the size-scale ladder, how large is one trillion? The simple answer is that one trillion is 1,000 times bigger than one billion, but let's look at this in terms of the comparisons we've been looking at. As far as stacks of money goes, one trillion $1 bills makes a very valuable pile that's over 63,000 miles long—that's 2.5 times the distance around the Earth! And one trillion seconds is nearly 32,000 years. Compared to the 11.5 days for one million seconds and 32 years for 1 billion seconds, one trillion seconds is an incredibly long period of time.

One trillion seconds is nearly 32,000 years.

Just for fun, let's now think about trillions using a completely different method of comparison. Given that there are approximately 7.1 billion people currently alive on the planet, if we were to evenly divide up the surface area of the Earth and give a portion to each person, we would all receive a plot of land (or more likely water) that's about 10 soccer fields in size.

What if there were 1 trillion people on the planet? Then we'd each get a chunk of land or water about the size of two tennis courts. While that's not a lot of surface area for each of us to live on, it shows that it is at least possible for 1 trillion people to simultaneously exist on the planet. Of course, there's no way everybody would have enough to eat or drink or who knows what else, but it does provide some perspective on the magnitude of 1 trillion.

How to Think About Even Bigger Numbers

How about even bigger numbers like one quadrillion (that's 1,000 trillion)? What's the best way to think about them? We could, once again, just continue what we've been doing. For example, if there were one quadrillion people on the planet, we could each be given a portion of Earth's surface equivalent to the area of about 10 sheets of printer paper—definitely too cozy for my taste. One quadrillion stacked dollar bills would extend nearly from the Earth to the Sun, and one quadrillion seconds is over 30 million years!

But since one quadrillion is the same as as one million billion, we can also think about its magnitude in a slightly different way by combining the comparisons we've already come up with for one million and one billion. For example, if we want to think about the magnitude of one quadrillion, we can imagine that the width of each and every one of the one billion $1 bills in our stack of money extending the width of Earth's atmosphere suddenly expands in size to the length of a football field. The resulting huge height of this stack would be the same as the height of one quadrillion $1 bills.

As you can see, there's no single "best" way to do any of this. Use whatever comparisons speak to you and help you develop intuition for the relative sizes of large numbers. Because astronomical numbers show up all the time in real life, and it pays to have a firm grasp on what they mean.

Wrap Up

OK, that's all the math we have time for today.

Please be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Money stack image courtesy of Shutterstock.

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