How to represent a small change in a larger number

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SUMMARY

The discussion centers on representing small changes in numerical values, specifically in the context of calculating the wavelength of Doppler-shifted light. The example provided is 500.0000000000139x10^-9 m, which is a slight variation from the initial wavelength of 500x10^-9 m. Participants explore alternative notations to express small increments without using a plus sign, suggesting that compact forms like scientific notation can effectively convey these changes. The conversation highlights the need for clear and concise mathematical representation in scientific contexts.

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  • Understanding of scientific notation
  • Familiarity with the Doppler effect in light
  • Basic knowledge of wavelength measurements
  • Experience with numerical precision in calculations
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  • Research advanced scientific notation techniques
  • Learn about the Doppler effect and its applications in physics
  • Explore numerical representation in computational tools like MATLAB or Python
  • Study the significance of precision in scientific measurements
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Students in physics, mathematicians, and anyone involved in scientific research requiring precise numerical representation and understanding of the Doppler effect.

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
 
Mathematics news on Phys.org
You could represent only the value of the change (e.g. "a total change of +139x10something")
 

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