# Failure of dimensional analysis for a rule

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Day 2023년 9월 21일
댓글: Day 2023년 9월 27일
Hi,
I have a rule y=x^0.35. x has the dimension of mass. An error message showed up saying that the exponent must be an integer constant. How can I handle this situation as this rule is very important in my model?
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Day 2023년 9월 21일
The model was developed using the Simbiology app without writing codes.
Torsten 2023년 9월 21일
편집: Torsten 2023년 9월 21일
Can't you assign a unit to y instead of letting Simbiology compute it for you as kg^0.35 ? And why is it possible if the exponent is an integer ? Are you sure that this is really a dimensional problem ?

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### 채택된 답변

Arthur Goldsipe 2023년 9월 21일
When you enable dimensional analysis (or unit conversion) in SimBiology, fractional exponents can only be applied to dimensionless quantities. So you could write your rule as y=y0*(x/x0)^0.35, where x and x0 have the same units, and y0 is the value of y when x=x0.

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### 추가 답변 (1개)

Walter Roberson 2023년 9월 21일
I am baffled about what unit (grams ^ 0.35) would be. Should that be interpreted as (grams ^ (35/100) so that the unit would be "the 100'th root of grams to the 35'th power" ? Or should it be interpreted as (grams ^ (7/20)) ? so that the unit would be "the 20'th root of grams to the 7'th power" ?
Mind you, I also struggle with the physical meaning of something like y = sqrt(x) when x is mass.
If this is a situation of "never mind the dimensional continuity for now, the math works out" then you are going to have to strip the units from the item, make the math transformation, and add units back to the result.
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Walter Roberson 2023년 9월 22일
Hmmm, it appears that people do find uses for odd units; https://www.reddit.com/r/askscience/comments/2v4gv5/the_square_root_of_a_kilogram/
Day 2023년 9월 27일
@Arthur Goldsipe Thank you very much

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