"I eat half an apple for breakfast."
Translation:Jem pół jabłka na śniadanie.
It's close, but you used "połowa" in Nominative, although it should be in Accusative, as needed by "jeść". "Jem połowę jabłka na śniadanie".
With something relatively small, like an apple, the diminutive form "połówka" (Jem połówkę jabłka) sounds better to me, but it doesn't mean that "połowa" is wrong.