Final answer:
The numbering system mentioned is the serial-unit numbering system, where a patient receives a new number for each visit but all records are filed under the most recent number.
Step-by-step explanation:
The numbering system described in the question is known as the serial-unit numbering system. In this system, each time a patient visits the healthcare facility, they are assigned a new unique number for that encounter. However, when it comes to filing their medical records, all of their documents are filed under the most recent number assigned. This latest number, then effectively becomes the patient’s master number for all subsequent healthcare visits and associated records.