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How Can We Think About Really Large Numbers?

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By

Courtney Taylor

Courtney Taylor

Professor of Mathematics

- Ph.D., Mathematics, Purdue University
- M.S., Mathematics, Purdue University
- B.A., Mathematics, Physics, and Chemistry, Anderson University

Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra."

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Updated on April 17, 2020

The Piraha tribe is a group living in the jungles of South America. They are well known because they do not have a way to count past two. According to Daniel L. Everett, a linguist and professor who spent decades living among and studying the tribe, the Piraha have no number words to distinguish between these two numbers. Anything more than two is a “big” number.

Most people are similar to the Piraha tribe. We may be able to count past two, but there comes a point where we lose our grasp of numbers. When the numbers get big enough, intuition is gone and all we can say is that a number is "really big." In English, the words "million" and "billion" differ by only one letter, yet that letter means that one of the words signifies something that is a thousand times larger than the other.

Do we really know how big these numbers are? The trick to thinking about large numbers is to relate them to something that is meaningful. How big is a trillion? Unless we’ve thought of some concrete ways to picture this number in relation to a billion, all that we can say is, "A billion is big and a trillion is even bigger."

## Millions

First consider a million:

- One million is a thousand thousands.
- One million is a 1 with six zeros after it, denoted by 1,000,000.
- One million seconds is about 11 and a half days.
- One million pennies stacked on top of each other would make a tower nearly a mile high.
- If you earn $45,000 a year, it would take 22 years to amass a fortune of 1 million dollars.
- One million ants would weigh a little over 6 pounds.
- One million dollars divided evenly among the U.S. population would mean everyone in the United States would receive about one-third of one cent.

## Billions

Next up is one billion:

- One billion is a thousand millions.
- One billion is a 1 with nine zeros after it, denoted by 1,000,000,000.
- One billion seconds is about 32 years.
- One billion pennies stacked on top of each other would make a tower almost 870 miles high.
- If you earn $45,000 a year, it would take 22,000 years to amass a fortune of one billion dollars.
- One billion ants would weight over 3 tons—a little less than the weight of an elephant.
- One billion dollars divided equally among the U.S. population would mean that everyone in the United States would receive about $3.33.

## Trillions

After this is a trillion:

- One trillion is a thousand billions, or equivalently a million millions.
- It is a 1 with 12 zeros after it, denoted by 1,000,000,000,000.
- One trillion seconds is 32,000 years.
- One trillion pennies stacked on top of each other would make a tower about 870,000 miles high—the same distance obtained by going to the moon, back to Earth, then to the moon again.
- One trillion ants would weigh over 3,000 tons.
- One trillion dollars divided evenly among the U.S. population would mean that everyone in the United States would receive a little over $3,000.

## What’s Next?

Numbers higher than a trillion are not talked about as frequently, but there are names for these numbers. More important than the names is knowing how to think about large numbers. To be a well-informed member of society, we really should be able to know how big numbers like a billion and trillion really are.

It helps to make this identification personal. Have fun coming up with your own concrete ways to talk about the magnitude of these numbers.

View Article Sources

Everett, Daniel. (2005). "Cultural Constraints on Grammar and Cognition in Piraha: Another Look at the Design Features of Human Language."

*Current Anthropology,*vol. 46, no. 4, 2005, pp. 621-646, doi:10.1086/431525*"**How Many Thousands Make 1million?**"*University of Regina, mathcentral.uregina.ca.Milliman, Hayley. “How Many Millions in a Billion? Billions in a Trillion?” blog.prepscholar.com.

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*How Much Is a Billion?*" www.plainenglish.co.uk.“How Much Is a Trillion?”NPR, 8 Feb. 2008.

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Taylor, Courtney. "Millions, Billions, and Trillions." ThoughtCo, Apr. 5, 2023, thoughtco.com/millions-billions-and-trillions-3126163.Taylor, Courtney. (2023, April 5). Millions, Billions, and Trillions. Retrieved from https://www.thoughtco.com/millions-billions-and-trillions-3126163Taylor, Courtney. "Millions, Billions, and Trillions." ThoughtCo. https://www.thoughtco.com/millions-billions-and-trillions-3126163 (accessed September 3, 2024).