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You don't have to put units throughout your work as long as you have the correct units at the end, but including the units can help you if a TA is correcting your work then you can get partial credit if you didn't have the correct units at the end.
I'd also recommend putting the units as if it comes to partial credit for a question it might help who ever is grading it see what and where you went wrong. It could possibly improve your chances of getting more credit for a problem that would not have gotten it otherwise.
I'm not sure if points will be taken down but, personally, it helps me make sure that I am not using incorrect units in a given area. Also, I do believe we get partial credit in places and I think that having units all the way through would ensure you get all the points you deserve.
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