# Really Really Big Numbers

Some people can take information and understand it and apply it themselves to the world around them. I need an example to really get the hang of something. So here is some information, and then and example.

## Scientific Notation

When sciency types talk about big numbers and even when people on the news talk about big numbers they use scientific notation as a way of avoiding having to say overly long numbers. Scientists are nothing if not efficient. So instead of saying 2 billion 500 million or writing 2,500,000,000. They’ll say 2.5 billion, or 2.5 X 109. Or “two point five times 10 to the 9th power.”

Quite simply, you’re separating the information of the number from the magnitude of the number to make it easier to both understand and compare to other numbers. Here is better explaination from Ted Ed.

Now that video makes it seem like Fermi’s estimation of the bomb blast of 10kilotons is the same as the actual blast of 20 kilotons. While the actual yield was twice (2x) his estimation, if it was ten times his estimation he would have been an oder of magnitude wrong. So on the grand scheme of things, he was pretty darn close.

## Sand grains vs Stars vs Water Molecules

There is an old conundrum that asks, are there more sand grains on the earth than Stars in the sky? Until astronomers got the Hubble Telescope, which orbits Earth in space, it was hard to get a good idea of how to estimate the number of stars in the sky. “It turns out that when you look up, even on a clear and starry night, you won’t see very many stars,” writes Robert Krulwich on his blog. “[David] Blatner says the number is a low, low “several thousand…” But with Hubble, you can see much much more.

Midsumer Night Milky Way over Tahoe. Photo by Barrett Donovan

Now the population of stars jumps enormously, to 70 thousand million, million, million stars in the observable universe (a 2003 estimate)… [Krulwich Wonders]

This article from the European Space Agency pegs the number of stars in the observable universe on the magnitude of 1022 or 1024. Compared to the estimated number of grains of sand on the earth (only about 7.5 x 1018) , there are more than enough stars to go around.

## Water Molecules

What really bakes Mr. Krulwich’s noodle is the idea that there are more molecules of water in just ten small drops than sand grains on the Earth or stars in the universe,

This is amazing to me. For some reason, when someone says million, billion or trillion, I see an enormous pile of something, a grand scene, great sweeps of desert sand, twirling masses of stars. Big things come from lots of stuff; little things from less stuff. That seems intuitive. [Krulwich Wonders]

So there you go. Three scales, the very small, the pretty big and the supremely hugely big, that all have unbeleviably large numbers, the biggest of which you can hold in your hand…

-Mike

Sources: