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Scientific notation 53030000

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4 Answers

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 100 is the same number (it hasn't changed in value).  So we can say that your original number 53030000 is now:

53030000.0 X 100

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 ~ 107.

53030000.0 X 100 would now be 5.303 X 107

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 5.3030000 X 107 as well as 001.05 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.

 

53030000. is the number in question.  For every position you move the decimal point left, that is a power of 10.  If you move it until the first digit is the only thing left of the decimal point, you will have shifted the decimal place left 7 positions.

53030000 is the same was 5.303 x 107, or 5.303 multiplied by 10 million.

In Scientific notation, you only have one digit to the left of decimal, and the rest of the digits are to the right, leaving out any unnecessary zeros. This is then multiplied by some power of 10, which can be determined by the number of places the decimal place moves. 

Given 53 030 000 (spacing for readability), if we move the decimal to the left 7 places , we get 5.3030000 time some power of 10. Since we moved the decimal 7 places, the power would be 7:

5.3030000 * 107 . But the zeros to the right don't provide us with any useful precision, so our answer is 5.303 * 107

Place the decimal after the first non-zero digit and then count the number of spaces to determine how much to raise ten by an exponent.

In your example:

5 3030000

You have 7 decimal places after the first number and you have to include up to the last non zero number after that.

So 5.303x107 is your answer.