Often in mathematics and also in science, you need to write down very big or very small numbers. Now you can do this the hard way, writing down something like:
Personally, I don’t like having to write down all those zeroes each time I want to write that number. And let’s face it, if you’re doing a problem using this number, chances are you will have to write it down a few times. Luckily, you can use exponential notation to write it in a much easier way. I can use a simple example to show you how to do it.
Say I have the number ‘500’. Now we all know that 500 is the same as “five lots of a hundred”. So I could write something like:
Or, if I wanted to be a bit more ‘mathematical’ about it, I could write:
Now we can take this one step further by writing the ‘100’ as a power of 10. This means we rewrite 100 as “ten to the power two” like this:
And congratulations – you’ve just rewritten ‘500’ in exponential notation. There’s a quick and easy way to do this without going through all the stuff I just explained – you just have to keep track of how many places you’ve moved the decimal point. So if I start with:
This is really:
which is also the same as:
since 
is equal to ‘1’.
Now what I can do is move the decimal point to the left, and for each place I move it, I increase the value of the power by 1. So:
This is a quick and easy way to get a number in exponential notation. Now we can go back to our original problem, which was to rewrite the following number in exponential notation:
What we do is move the decimal point to the left, until it’s on the right hand side of the leftmost digit, which is a ‘5’ in this case:
This means that we have moved the decimal point 10 places to the left, so we need to increase the power above the ‘10’ from ‘0’ to ‘10’:
