This way of writing a number is called scientific notation.
The number 0.0045 and 4.5 x 10^-3 are essentally the same. Notice that the 10^-3 is the same as 0.001 and so:
As the name says, it is just a different notation for the same number.
It is usually used because of significant figures, so we can know better how many significant figures we have.
The important part is to know the form we call scientific notation. The leadin number has to always be a number between 1 and 9.999..., It can't start with 0 nor 10 or higher. And it is followed by the 10 to the appropriate power.
Let's do two examples:
The number 0.000896:
We need to grap just the part of the number, 896, but it needs to be between 1 and 9.999, so we pick 8.98
Now, we need the appropriate power so the result it 0.000896. We can see that we need to multiply 8.98 by 0.0001 to get this, and 0.0001 is the same as 10^-4, so:
Another example can be 863,000. the appropriate leading number is 8.63, so we need to to multiply it by 100,000 to get it correctly. This is the same as 10^5, so:
