How is a female questioner to expiate for the oath she swore by Allah —that she does not know the price of her sister's clothes— despite her prior knowledge of the price?

Allah does not hold one accountable for a laghw (frivolous) oath, such as saying "No, by Allah" or "Yes, by Allah." This type of oath does not entail the rulings of an oath nor does it require expiation, due to the Almighty's saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths." (Quran 5:89) As for the yamin ghamus (perjured oath), which is intentionally swearing a false oath, it is one of the grave sins and immerses its perpetrator in sin. The most cautious approach for it is to combine repentance with expiation.