Whether the extended sound is there or not is important in distinguishing words, and there isn’t a way to know whether it should be in a word or not. It’s simply a part of the identity of the word. You are right in that う is used to denote some kinds of extended sounds (the other kind being い as in せんせい). For words that contain u and o sounds, we have to remember whether or not the sound-extending う is there, since its presence or absence will result in different words. It’s definitely tough to hear the difference, and sometimes it can be very ambiguous since the length also depends on how fast the speaker is talking. However, as you learn more and more Japanese, you’ll become better at processing context, which is another vital clue in determining the identity of a word. Context is even more important when we’re dealing with homophones, which happen to appear a lot in Japanese. :) Some examples: 数字（すうじ） vs 筋（すじ） 上司（じょうし）vs 女子（じょし）

you can tell by tuning your ears to hear the final う and by learning vocab and their spellings