What is this: 53030000 in scientific notation?

I don't normally tutor in math, unless I'm teaching electronics. But this looks like fun :-).

The first thing I would have my students do is to ask "Does it have a decimal point?" If so, we'll skip this step, if not, GIVE IT ONE. Since this number does not already have a decimal point, let's give it one. We'll also add an extra zero after the decimal point just to make it more 'visible.'

53030000 will become 53030000**.0**

The reason I do this is because I feel it is easiest to think about scientific notation as nothing more than manipulating (moving) the decimal point around. Now, if you are a math major, you may be taught to think and feel differently :-).

The next thing to remember is that any number times **10**** ^{0}** is the same number (it hasn't changed in value). So we can say that your original number 53030000 is now:

53030000**.0** X **10 ^{0}**

While there are different 'flavors' of scientific notation, the bottom line is to convert the number into another number which is
the product of **10 to some power**. Standard (or what they call 'normalized') scientific notation aims at ending up with a single number somewhere
between zero and ten (but not zero or ten).

The easiest way to do that is to move the decimal either to the left (for large numbers like you have here) or to the right (for small numbers like
**0.**000567). Each time you move the decimal to the **left**, your exponent (power) number will need to
**go up** and each time you move the decimal to the **right**, the exponent needs to go
**down**.

With your number, **53030000.0**, you will end up with **5.**303 times 10 to some power (notice that
**5** is somewhere between zero and ten). In order to move the decimal over enough, you will need to move it
7 places. That would mean you would increment (increase) your exponent by 7. Since we started with an exponent of zero, this would be an easy one ~ 10^{7}.

53030000**.0** X 10^{0} would now be **
5.**303 X 10^{7}

Notice that any zeros "away from the decimal point" can be dropped because they are considered 'insignificant' in the overall value of the number. This can also be applied to leading zeros preceding the decimal point. It would be considered bad style to say 5.303**0000** X 10^{7 }as well as **00**1.05 X 10^{-3}.

I'm certain math teachers will give you a much better (mathematical) answer, but here's my blue collar version. I hope it helps.