Question 1098249: Explain why 0.75 x 10^5 is not written in correct scientific notation. Write the number correctly using scientific notation.
Answer by math_helper(2461)   (Show Source):
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A number expressed properly in scientific notation has a characteristic (the part to the left of the decimal point) between 1 and 9, inclusive.
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Your number is written:
(it was written above as well)
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Given a number, you keep track of how many places to the left (or right) you need to move the decimal point to get the number to the left of the decimal point to be between 1 and 9 inclusive, then that number of places you moved the decimal point becomes the exponent (moving it left results in a positive exponent, moving it right results in a negative exponent). In the case of 0.75x10^5, which is partly, but incorrectly written, we need to move the decimal point one place to the right, so we subtract one from the exponent.
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Here are some more examples:
Write the following in scientific notation:
1) 0.000011
2) 56789 (notice that the decimal point would be written just after the 9)
3) 77.665544
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Answers:
1) 
2) 
3) 
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In response to your second message. No, 0.75 x 10^5 is NOT proper scientific notation. It is not proper because the leading digit 0, does not fall between 1 and 9, inclusive. You may now be saying to yourself "that's silly" but that is the agreed upon convention in the mathematical community for proper scientific notation. If your number is proper, then so is 0.00075x10^8 and now we have yet another way to write it "properly." Don't fight the convention, there are good reasons for things to be presented in a uniform way.
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