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:

_{}

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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’:

_{}