Is Scientific Notation Only for Approximating Large Numbers?

In summary, slide rules were commonly used in the past for calculations, and scientific notation was used to reduce numbers to a manageable amount of digits. With the advent of modern calculators, slide rules and scientific notation are no longer necessary. However, scientific notation can still be useful in determining the number of significant digits in a calculation. Slide rules are now considered collectibles, but due to their abundance, they do not hold much value.
  • #1
Holocene
237
0
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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  • #2
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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  • #3
Integral said:
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:
 
  • #4
Integral said:
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?
 
  • #5
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!)
 
  • #6
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What is scientific notation?

Scientific notation is a way of writing very large or very small numbers in a more compact form. It consists of a number between 1 and 10 multiplied by a power of 10. For example, 500,000 can be written as 5 x 10^5 in scientific notation.

Why is scientific notation used?

Scientific notation is used to make very large or very small numbers easier to read and work with. It also allows for easier comparison between numbers that have different orders of magnitude.

How do you convert a number to scientific notation?

To convert a number to scientific notation, move the decimal point to create a number between 1 and 10. The number of places you move the decimal point will determine the power of 10 in the scientific notation. If the decimal point is moved to the right, the power will be negative, and if it is moved to the left, the power will be positive.

What is the purpose of the exponent in scientific notation?

The exponent in scientific notation represents the number of times the decimal point was moved to create the number between 1 and 10. It indicates the order of magnitude of the number, making it easier to compare and work with very large or very small numbers.

How is scientific notation used in science?

Scientific notation is used extensively in science, particularly in fields such as physics, chemistry, and astronomy. It allows scientists to work with extremely large or small numbers that are often encountered in these fields, such as the mass of a planet or the size of an atom.

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