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Exponential Notation

Practical ways of talking about quite big numbers

When talking about quite big numbers, such as how many stars there are in the galaxy, it's useful to have a reasonable way of expressing them. The history of talking about big numbers ran into trouble quite early on. Although everyone agreed on how many a million was, there was a already a difference of opinion about how many a "billion" was, even across from one side of the Atlantic to the other and from period in history to the next, and besides if you were doing a business transaction and you'd got a cold, you could end up with some unexpected results. Plus, for amounts bigger than a million-million, it all gets a bit confusing in that kind of word-usage. Latin prefixes fare a bit better, so hard discs can be conceivably in megabytes, gigabytes, terabytes, petabytes, exabytes, zettabytes, yottabytes, [more] but even so it still gets a bit awkward. So, for the practical purposes of talking about quite big numbers, exponential notation is the preferred scientific language.

What happens is that 10x10x10x10x10x10
is a million, and in saying that the "10" is mentioned
six times. So, a million is 10^6 or 10^{6}, or to put it
another way, 1,000,000 has six zeroes, so it's 10^{6} (ten
to the power of six), or on a scientific calculator it's 1E6

This comes in very handy for
talking about things like the weight of the planet earth 5.972 x 10^{24} kilos, or the
power output of the sun 3.9 x 10^{26}
watts, or the speed of light
3 x 10^{8}. Number of stars in the galaxy is estimated to
be about ten thousand million, so that's 10^{10}.
Astronomically large numbers can be easily expressed, and
mathematically large numbers such as a googol (10^{100}) can too, to some extent.

As a practical example, see the working out of gravity on other planets

Exponential notation also allows talk about very small numbers, for example how much an atom weighs, or how much electricity there is in a single electron.

This is done by the fact that a
thousandth is 10^{-3} and a millionth is 10^{-6}.
By this means it's possible to say things like "an electron
weighs 9.109 x 10^{-31} ", without being lost for
words.

Other useful concepts of this ilk: How logarithms work