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How can we understand the meaning of large numbers like "a million million?"

I'm a 6th grade Science teacher. How do I explain "million million" to my students? For example, light travels 9.5 million million kilometers in a year.

This is a tough one! Numbers in astronomy are sometimes so big that they completely dwarf all other types of human experience, so it can be hard for people to relate to them.

The best way I know of to explain large numbers is to imagine taking something from everyday life that's extremely small and seeing how big it gets when you pile it up on top of itself over and over again. For example, a piece of paper is very thin... on the order of 0.005 inches thick. But if you took a trillion pieces of paper (i.e. a million million) and piled them on top of each other, your pile would be 127,000 kilometers high. If you then took that pile, wrapped a giant rubber band around it to hold it together, and stretched the pile around the Earth's equator, it would wrap around the Earth a little over three times! It's still hard to imagine, but at least this technique gives you a way to relate a "million million" to two things you're familiar with: the thickness of a piece of paper and the distance around the Earth.

Another way to understand large numbers is to imagine how long it would take to count to them. For example, if you're able to count one number every second, and keep on counting continuously without stopping for breaks, then it would still take you over 30,000 years to count to a million million. The famous prehistoric cave paintings at Lascaux in France are a little over 15,000 years old. So if the people who made those paintings had started counting then and lived until today, they would be about halfway to a million million!

November 2004, Dave Rothstein (more by Dave Rothstein) (Like this Answer)

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