Q.Write short notes on the following.

Step 1 (a. Unit). A unit is an arbitrarily chosen standard of measurement of a quantity, accepted internationally, used as the reference for comparison. Measurement is comparison: saying a rope is '10 metres' means it is 10 times as long as the internationally-accepted 1-metre standard. Units split into fundamental (base) units, measuring the seven fundamental quantities directly (metre, kilogram, second, ampere, kelvin, mole, candela), and derived units, built by multiplying/dividing powers of the base units (e.g. m s$^{-1}$ for velocity).

Step 2 (b. Rounding off). Rounding off trims a calculated result's excess digits down to the number of significant figures the original data actually justifies, using five rules: a dropped digit $<5$ leaves the preceding digit unchanged (e.g. $7.32\to7.3$); a dropped digit $>5$ raises the preceding digit by 1 ($17.26\to17.3$); a dropped digit of exactly $5$ followed by non-zero digits always raises the preceding digit ($7.352\to7.4$); and for a dropped digit of exactly $5$ (or 5 followed only by zeros), the 'round-to-even' rule applies -- unchanged if the preceding digit is already even ($3.45\to3.4$), raised by 1 if it is odd ($3.35\to3.4$) -- which avoids biasing repeated roundings in one direction. …

• Confusing 'dimensionless' with 'unitless' -- a dimensionless quantity like angle (radian) can still carry a named unit even though its dimensional formula is trivial. …