Significant Figures for Exponents and Logs [closed]








**Closed.** This question is [off-topic](/help/closed-questions). It is not currently accepting answers.
 
 






---








 **Homework questions** must demonstrate some effort to understand the underlying concepts. For help asking a good homework question, see: [How do I ask homework questions on Chemistry Stack Exchange?](https://chemistry.meta.stackexchange.com/questions/141/how-do-i-ask-homework-questions-on-chemistry-stack-exchange)




Closed 3 years ago.








[Improve this question](/posts/128430/edit) 



What are the Sig Fig rules for exponents and logs. Ex. if I have 10^-3.83, or log(4.32) how should the answer be represented





> 
> if I have 10^-3.83
> 
> 
> 


-3.83 is less than -3.82 and more than -3.84. If we raise 10 to those powers, we get:


$$10^{-3.82} = 0.000151$$
$$10^{-3.84} = 0.000144$$


So the answer is 0.00015 or $\pu{1.5e-4}$



> 
> if I have [...] log(4.32)
> 
> 
> 


$$\log(4.31) = 0.6344$$
$$\log(4.33) = 0.6364$$


So the answer is 0.64.



> 
> What are the Sig Fig rules for exponents and logs?
> 
> 
> 


Once you use exponents and logs a lot, you might also know some calculus to support a better model of error propagation. If not, the rule for logs is that the error is equal to the error of the argument divided by the argument. The rule for exponentials is that the error is equal to the error of the exponent times the value of the exponential. Very few introductory textbooks bother to state these, though. 


 1