## Millions, billions and trillions

A rough estimate of the number of grains of sand on this stretch of beach will lead you to an astronomical number, one that also gives you a sense of how many stars are in, say, 10 galaxies. Photo:
Suneel Raghavendra

What’s the difference between a million and a billion? If you answer, “Just one letter,” you are literally correct, and for most of us they are just very big numbers that we cannot grasp. Until recently, they had no use. A shepherd might need to count a hundred sheep, but never a thousand, let alone a thousand thousand, which is a million. We all know billionaires are very rich, but do you realize that a billion dollars can buy 1,000 million-dollar homes?

In science we often deal with unimaginably huge numbers. For example, we estimate that our Milky Way galaxy, like most galaxies, contains about a hundred billion (100,000,000,000 = 1011, because 11 zeros) stars. Of course, we haven’t counted them all, but we can count those in a small patch and multiply by the ratio of areas.

Coincidentally, this is also roughly the number of galaxies in the visible universe and the number of neurons in your brain!

In science we often make rough estimates –  we don’t always need to be precise. On a beach, I would teach my kids to estimate the number of grains of sand. This is much easier with meters than with inches, feet and yards (a yard is 0.91 meters). Guesstimate the length, width and depth as, say, 100 meters, 10 meters, and 1 meters, so the volume is 1,000 (103) cubic meters. Roughly.

Since 1 meters is 1,000 millimeters, there are a billion cubic millimeters in a cubic meter and so a trillion (1012) cubic millimeters on the beach. Now you are all done: a few trillion grains of sand. If each grain of sand were a dollar, that is the national debt! An astronomical number, but not infinite!

Speaking of astronomical, we think that most stars have planets. Now — pure guesses: Even if only 1 percent of the planets have conditions good for life, and only 1 percent of those actually have some form of life, that is still 10 million planets in our galaxy with life. If the probability that a planet with life evolves to be an advanced society is 0.1 percent, that makes 10,000 such civilizations in our galaxy. Ours may be the only one, but that seems unlikely.

But don’t worry, the galaxy is so big that it is extremely unlikely that extraterrestrials are closer than 100 light-years (500 trillion miles) away. At that distance they could be listening to World War I news on the radio, and probably, wisely decide to leave us alone.

This is a version of an article that originally appeared in Positively Naperville.