Meters to the -3rd Power: 5.1*10^-5m

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The discussion centers on the dimensional analysis of multiplying meters by meters to the power of negative three. When multiplying 5m by 5m^-3, the result is 25m^-2, which can also be expressed as 25 per square meter. The term "per meter cubed" refers specifically to the unit m^-3, while m*m^-3 simplifies to m^-2. This clarification helps in understanding the units involved in calculations related to number density and other physical measurements. Accurate unit conversion is essential for correct scientific calculations.
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What would meters*meters^-3 be?

Ex: 5.1*10^-5m(1.314*10^18m^-4)

[m=meters]
 
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It would be read as "per meter cubed." Number density has this dimension, e.g. "100 molecules per meter cubed."

- Warren
 
OK but..

I have to do a calculation multiplying m and m^-3 and I don't know what unit to use for the answer.

Say..5m*5m^-3= 25..what unit?

Also, when you say "per meter cubed", are you talking about m^-3? or m*m^-3?

Thanks for your response.
 
per meter cubed is 1/m^3, but m*m^-3 is m^-2 or 1/m^2
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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