If by "radioactive" you mean "ever emits radiation" then yes, a small amount of radioactive water can dilute into a large volume of still-radioactive water. By

If by "radioactive" you mean "ever emits radiation" then yes, a small amount of radioactive water can dilute into a large volume of still-radioactive water. By if you use that definition you yourself would be considered "radioactive" as you are always walking around carrying quite a few radioactive isotopes, including Carbon-14 (as made famous by "carbon dating" from geology) and Potassium-40. As pdonis notes, radioactive contaminants dilute just as well as any other contaminant in water. Assuming it more-or-less evenly mixes within the Pacific Ocean, you could essentially dump all of Fukushima into that ocean and not see large changes in overall ocean radioactivity.