### Measurement and Errors

goals
A micrometer screw gauge has a negative error of 7 divisions. While measuring the diameter of a wire the reading on main scale is 2 divisions and $78^{th}$ circular scale division, coincides with base line. The number of divisions on main scale are 10 to a centimetre and the circular scale has 100 divisions.
N divisions on the main scale of vernier callipers coincide with (N+1) divisions on the vernier scale. If each divisions on the main scale of a units, determine the least count of instrument.
Subtract $2.5 \times {10}^{4}$ from $3.9 \times {10}^{5}$ and give the answer to correct number of significant figures.
Two rods have lengths measured as $\left( 1.8\pm 0.2 \right)m$ and $\left( 2.3\pm 0.1 \right)m$. Calculate their combined length with error limits.
You have a bag of cotton and an iron bar, each indicating a mass of $100kg$ when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?