Scientific Notation question

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Obviously, if you wanted to express 500,000 in Scientific Notation, you would get:

5 x 10^5

My question is, what if you were asked to express 570,098?

Move the decimal 5 places to the left, and you'd get 5.70098. Apply Scientific Notation, and you get

5.70098 x 10^5

However, this expression actually contains MORE numbers than the original number, which is not the goal of Scientific Notation.

So is SN just for expressing approximations of large numbers??? Should I have rounded 570,098 to 570,000???

Thanks a lot.
 
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Integral
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Scientific notation was most useful in the days of slide rules. At absolute max a slide rule can only carry 4 digits. To do a calculation with a slide rule you reduced all numbers to scientific notation with 3 or 4 digits then used the slide rule to perform the basic operations and in a separate calculation determined the order of magnitude by combining the powers of 10.

The curse and blessing of modern calculators is that this type of thinking is no longer necessary. You can just poke in the numbers hit the button and copy down every thing in the display. Of course the fact that most of the digits in the display of a calculator is useless noise does not bother most students for even a second.

A useful function of Scientific notation would be to make it clear how many significant digits you have.
 
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Of course the fact that most of the digits in the display of a calculator is useless noise does not bother most students for even a second.
It always makes you wonder about a student's comprehension of 'experimental error' when they give answers to 8 or 9 significant places (or 12 for big calculators) which they derived from experimental values they measured to only 2 or 3 places at best. :cry:
 
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Scientific notation was most useful in the days of slide rules. At absolute max a slide rule can only carry 4 digits. To do a calculation with a slide rule you reduced all numbers to scientific notation with 3 or 4 digits then used the slide rule to perform the basic operations and in a separate calculation determined the order of magnitude by combining the powers of 10.

The curse and blessing of modern calculators is that this type of thinking is no longer necessary. You can just poke in the numbers hit the button and copy down every thing in the display. Of course the fact that most of the digits in the display of a calculator is useless noise does not bother most students for even a second.

A useful function of Scientific notation would be to make it clear how many significant digits you have.
I never heard of slide rule's until the other day when my aunty got me one from 1962. I had no idea what it was...then I worked it out.
Are they worth anything?
 
HallsofIvy
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Just curiosities now. A calculator can do anything a slide rule can, faster and more accurately. (I used to be able to find square roots on an abacus!)
 
D H
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