Step 1: Concept The least count is the smallest value that can be accurately measured by a surveying instrument.
Step 2: Meaning Most standard vernier theodolites have a least count expressed in seconds or minutes of an arc.
Step 3: Analysis A common vernier theodolite has a least count of 20 seconds ($20''$). To convert seconds to minutes, we divide by 60 ($20/60 = 1/3$). This equals approximately 0.33 minutes.
Step 4: Conclusion Therefore, 0.33 minutes is the equivalent least count.
Final Answer: (A)