Significant Figures And Errors

Error propagation in NCERT Class 11, Chapter 2 states that when two quantities are multiplied, the maximum fractional error in the product equals the sum of the fractional errors of the individual quantities, and the same holds for percentage errors. If $Z=A\times B$, then $\frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$. Converting to percentages and substituting, the maximum percentage error is $2\%+3\%=5\%$. This additive rule reflects the worst case where both individual errors push the result in the same direction. The value 1 percent is wrong because it subtracts the errors, which would apply only to a lucky cancellation, not the maximum error. The value 6 percent is wrong because it multiplies the two percentages, which has no basis in propagation rules. The value 2.5 percent is wrong because it averages the errors instead of summing them. The same additive rule extends to division, where fractional errors of numerator and denominator still add, and to powers, where the fractional error is multiplied by the exponent; recognising which rule applies is essential in experiments like finding density or Young's modulus. This is a maximum or worst-case estimate; a statistical treatment combining errors in quadrature would give a smaller typical error, but NCERT uses the simpler additive bound at this level. A plausibility check confirms that combining two uncertain measurements can only make the result less certain, so the total error of 5 percent must exceed each individual error, which it does.