Question about the interpretation of coefficients

Question about the interpretation of coefficients. Good morning, I have a question about the interpretation of coefficients when independent variables are standardized. When they are not standardized: Bi --> I understand that an increase of one unit in Xi, while keeping the rest of the variables constant, results in an increase of Bi units in Y. When they are standardized, how are the coefficients interpreted? In the example of Multiple Linear Regression for GPA, how would the interpretation of the coefficient associated with SAT be? Would it be correct to say --> Holding the rest of the variables constant, an increase of one standard deviation in SAT results in an increase of 0.17 points in GPA (for which I would need to check the value of the standard deviation of SAT)? Greetings and thanks in advance.