Partials are the normal case for any order larger than the size resting at your price. What happens to the leftover is entirely determined by your instructions: a day-order keeps working, an immediate-or-cancel kills the rest, a fill-or-kill would have refused the trade altogether.
They also change your risk arithmetic mid-trade. Your stop distance was sized for a full position; with a third of it on, both your risk and your intended reward are a third of plan.
Example: you buy 3,000 shares with a limit at 22.10. You get 900 at 22.10 and the offer lifts to 22.16. You now hold 900 shares with a 2,100-share remainder working. Averaging in at 22.16 raises your cost basis to roughly 22.142 and invalidates the 22.05 stop you had planned.
Related: fill-rate, average-fill-price, immediate-or-cancel, all-or-none