At Apex Precision Manufacturing, you are working as a Quality Assurance Technician. During your onboarding, you learned that all database entries must adhere to strict formatting standards. Specifically, you are required to log extreme measurements—such as a production batch size of {}4{,}000 units and a micro-component clearance tolerance of {}0.004 mm—using scientific notation.

Your supervisor has asked you to draft a brief training response for the division's standard operating procedure (SOP) manual. Write a short essay that details the exact steps and mathematical rules you must recall and apply to convert both {}4{,}000 and {}0.004 into scientific notation.

In your response, ensure you:

1. State the final scientific notation representation for both {}4{,}000 and {}0.004.
2. Detail the step-by-step conversion process for the number {}4{,}000, explaining where the decimal point starts, how many places and in what direction it must move to create the first factor (a number greater than or equal to ${}1$ but less than ${}10$), and how this determines the sign of the exponent on ${}10$.
3. Detail the step-by-step conversion process for the number {}0.004, explaining where the decimal point starts, how many places and in what direction it must move to create the first factor (a number greater than or equal to ${}1$ but less than ${}10$), and how this determines the sign of the exponent on ${}10$.
4. Recall and state the general mathematical relationship/definition (e.g., positive vs. negative powers of ${}10$) that justifies why a number greater than ${}1$ has a positive exponent and a number between ${}0$ and ${}1$ has a negative exponent.