To estimate the diameter of the thread, I would wind the thread tightly and uniformly around a cylindrical object (like a pencil) in adjacent turns. I would count the number of turns (say, n) and measure the total length covered by these turns using the metre scale (say, L). The diameter of the thread would then be calculated as: Diameter = L/n. This method works because when the thread is wound tightly, the total length equals n times the diameter. Taking multiple readings and averaging improves accuracy.

No, it is not possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale. While increasing divisions reduces the least count (pitch divided by number of divisions), there are practical limitations. The mechanical errors like backlash error and irregularities in the screw threads cannot be eliminated. Also, the human eye has limited resolving power and cannot distinguish extremely small divisions. Beyond a certain point, increasing divisions does not improve practical accuracy due to these inherent limitations.

A set of 100 measurements yields a more reliable estimate than 5 measurements because random errors tend to cancel out when more observations are taken. The mean value of a large number of measurements is closer to the true value. According to statistical theory, the precision of the mean increases with the number of observations. The standard error of the mean decreases as the number of measurements increases, making the result more trustworthy. With only 5 measurements, random errors may significantly affect the mean, while with 100 measurements, these errors average out.