How Big is a Billion?

All of us have difficulty imagining how many one billion of anything actually is. The following exercises may help your students better understand the enormity of the numbers involved when we talk about time and the Earth's history.

Exercise 1—Who Wants to Be a Billionaire?

How long would it take for you to become a billionaire?

Let's say that you are trying to save \$1,000,000,000 dollars and you are able to save your money at a rate of \$100 per day.

1,000,000,000 divided by 100 (dollars saved per day) = 10,000,000 days
10,000,000 days divided by 365 (days per year) = 27,397.26 years to reach \$1 billion

It will take a pretty long time to reach your goal! In fact, you would never get there in your lifetime. Nor would your children, grandchildren or great grandchildren. If you, and one descendent per generation, saved \$100 every day, and each of you lived for 90 years, it would take you and 304 generations of your descendants to save up one billion dollars.

Exercise 2—Counting

Let's say that your friend decides to count to 1 billion. How long will it take her?

She will be able to say the small numbers like 4 or 31 fairly rapidly, but most of the numbers between one and a billion are long and challenging to pronounce. When she starts counting the larger numbers like 467,051,372 she is really going to slow down (how long does it take you to say four hundred and sixty-seven million, fifty-one thousand, three hundred and seventy-two?). If we allow your friend just 3 seconds to say each number, which is probably faster than most of us could manage, and she takes no breaks at all, it will take her 3 billion seconds to finish counting.

3 billion seconds divided by 60 (seconds per minute) = 50,000,000 minutes
50,000,000 minutes divided by 60 (minutes per hour) = 833,333.333 hours
833,333.333 hours divided by 24 (hours per day) = 34,722.22 days
34,722.22 days divided by 365 (days per year) = 95.1 years is how long it will take your friend to count to 1 billion

Exercise 3—A Billion Step Hike

You decide to take a "billion step" hike. How many times would that take you around the equator?

Let's say that one step spans a 2-foot length—an average distance.
2 feet per step = 2 billion total feet traveled
1 mile = 5280 feet
2 billion (feet traveled) divided by 5280 (feet per mile) = 378,787.8787 total miles
The equator's circumference = 24,792.5 miles
378,787.8787 (total miles) divided by 24,792.5 (miles around the equator) = 15.278 times around the equator!

Extension: Ask students to work out a travel itinerary that is 378,787.8787 miles long and includes the names of the places visited and the distance between each leg of the journey. http://www.indo.com/distance/

Exercise 4—Stack of Paper

How much paper would it take to represent a billion? Or to represent the age of the Earth?

It would take 250 of the asterisk pages to show 1,000,000 asterisks. This can be used to help visually convey the enormity of the numbers used in talking about the history of Earth and life.

Try papering a wall with 1,000,000 asterisks, line the corridor to show a million or make a binder containing 250 asterisk pages (or 125 if double-sided).

Ask your students to solve problems, such as: how many pages would be needed to show the number of years that have passed since the dinosaurs went extinct, if each asterisk represents one year. (The dinosaurs went extinct 65 million years ago; if 250 pages equal 1 million years, then 65 times 250 = 16,250 pages.)

It would take 250,000 pages to show 1 billion asterisks. This is too many pages to paper the walls or make a binder with. In fact if you were to make up a binder that contained 2 million asterisks (500 pages per binder, single-sided) you would need 500 such binders to show 1 billion asterisks. But you can still help students visualize the quantity of paper it would take.

One ream of paper contains 500 sheets and typically stands 2 inches tall. So 250 sheets, about 1 inch thick, represents 1 million years. Ask your students to solve problems using that calculation, such as how thick the stack of asterisk pages would have to be to show the amount of time that has passed since the dinosaurs went extinct. (65 x 1 inch = 65 inches, or 5 feet, 5 inches.)

How tall would the stack have to be to show 1 billion years?
Remember, 1 million years = 1 inch.
1 billion divided by 1 million = 1000
You would need a stack of paper 1000 inches (or 83 feet, four inches) tall to show a billion years—that's as tall as an 8 story building!

How tall would the stack have to be to show the entirety of the earth's history?
1 billion takes 1000 inches of paper
The age of the Earth is 4.6 billion years
4.6 billion = 4,600 inches of paper
You would need a stack 4,600 inches tall to show the age of the Earth; that's 383 feet and 4 inches—the stack would be higher than a football field is long!

Extension: Assign your student to create their own "How Big is a Billion?" activity.