Q: How to state multiple approximate values within the same sentence?
The symbol tilda is often used to represent "approximately" but I am unsure which of the following is the correct usage:
1) The performance of method A and B improved by ~45% and ~38% resp.
2) The performance of method A and B improved by ~45% and 38% resp. (Here, I am assuming that tilda operates on both quantities)
While both are correct, I think it is preferable to use the first option, that is, use the tilda before both the quantities. This will ensure that there is complete clarity and readers do not misunderstand that the second value is an absolute value, not an approximate one. Therefore, I would recommend using this format:
The performance of method A and B improved by ~45% and ~38% respectively.
However, please check if your journal or the style manual used in your field recommends the use of any specific format.