Exponential Notation

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’: