Final answer:
The measured value using vernier callipers with a least count of 0.1 mm and a main scale reading of 10 mm is 10 mm. Significant figures are critical in communicating the precision of this measurement; the zero in 150 mm represents an estimated digit if it is based on estimation rather than a placeholder.
Step-by-step explanation:
The measured value obtained with vernier callipers with a least count of 0.1 mm and a main scale division of 1 mm is the sum of the main scale reading and the vernier scale coincidence. Given that the main scale reading before the zero of the vernier scale is 10 mm and that the zero division of the vernier scale coincides with a main scale division, the total measurement is precisely 10 mm, since no vernier divisions are added in this scenario.
Significant figures play a crucial role in indicating the precision of a measurement. If a measurement shows 150 mm, and the device measures in divisions of 1 mm, then the two known significant figures are 1 and 5, with the zero representing an estimated digit, provided it is the result of estimation and not simply a placeholder.
In terms of significant figures, when a value is reported, the certainty of each digit must be understood. If the measuring device, such as a ruler or vernier calliper, has smaller divisions, the number reported after the smallest marked division is an estimate. When measuring to the smallest marked division, the convention is to include one additional digit as the estimated value, which is also reflected in the reported error range.