Final answer:
The least count for an instrument with a vernier scale division of 0.5mm and a main scale division of 0.49mm is 0.01mm, reflecting the precision of measurements that can be made.
Step-by-step explanation:
To calculate the least count of an instrument where the value of one division of the vernier scale is 0.5mm and the value of one main scale division is 0.49mm, we need to understand how the vernier scale works. The least count is the smallest measurement that can be taken with the instrument and is determined by the difference between the values of one main scale division and one vernier scale division. In this case, the least count is 0.01mm (0.5mm - 0.49mm).
The least count is a critical concept in precision measurement, reflecting the limit to the finest measurement that can be made. This is related to the concept of significant figures, which are used to communicate the precision of a measurement. In our example, the least count of 0.01mm provides an indication of how accurately measurements can be made with the instrument.