How to represent a small change in a larger number

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It is also possible to use a scientific calculator or a programming language to handle large numbers and avoid the use of plus signs. In summary, there are a few options for representing small increases in a more compact form, such as using scientific notation or a scientific calculator.
  • #1
MCPO John-117
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Hey Everyone,

So I was doing some homework and one of my solutions was

500.0000000000139x10^-9 m

It wanted us to find the wavelength of doppler shifted light at a low speed and so the change is very small from the initial wavelength of 500x10^-9 m

I was wondering if there would be an easier way or some proper notation to write this small increase as a single number.

I could easily write 500nm+1.39x10^-11nm (5x10^-7m+1.39x10^-20m) but it doesn't feel right to have a plus sign in an answer. is there a notation that would help here?

is the notation compoundable?
how would you write
1000000000000000000000000000001.00000000000000000001
in a compact form other than
1x10^30+1+1x10^-20 ?

Thanks
 
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  • #2
You could represent only the value of the change (e.g. "a total change of +139x10something")
 

1. How do I represent a small change in a larger number using scientific notation?

The best way to represent a small change in a larger number using scientific notation is to use the original number as the coefficient and the small change as the exponent. For example, if the original number is 5,000 and the small change is 0.001, the scientific notation representation would be 5.000 x 10-3.

2. Can I use decimal notation to represent a small change in a larger number?

Yes, you can use decimal notation to represent a small change in a larger number. However, scientific notation is more commonly used because it allows for easier comparison of numbers with different magnitudes.

3. How can I calculate the percentage change of a small change in a larger number?

To calculate the percentage change, you can use the formula: (small change / original number) x 100. For example, if the original number is 50 and the small change is 5, the percentage change would be (5 / 50) x 100 = 10%.

4. Is there a limit to how small of a change can be represented in a larger number?

There is no limit to how small of a change can be represented in a larger number using scientific notation. However, as the exponent gets larger, the number becomes more difficult to read and understand. It is important to use scientific notation only when necessary.

5. Can I use scientific notation to represent a small change in non-numerical data?

No, scientific notation is only used for representing numbers. It is not appropriate to use it for non-numerical data such as words or symbols.

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