Final answer:
The correct isolation precaution for a patient with active tuberculosis is airborne precautions, due to the disease's transmission through inhalation of infectious droplets.
Step-by-step explanation:
A nurse admitting a client who has active tuberculosis should implement airborne isolation precautions. This is necessary because tuberculosis is highly contagious and is spread through the inhalation of droplets containing tubercle bacilli, which can be expelled from an infected individual's respiratory system when they cough, sneeze, or spit. For effective isolation, it is recommended to use a specialised air handling and ventilation system known as a negative pressure room to prevent the spread of these infectious agents to other areas of the healthcare facility.