Significant Figures

When measured quantities are multiplied, the rule for significant figures states that the result must be rounded to the same number of significant figures as the least precise factor entering the product. Here the length 4.2 cm has two significant figures, while the width 2.51 cm has three, so the limiting factor is two significant figures. The raw arithmetic product is 4.2 × 2.51 = 10.542 cm^2. Rounding this to two significant figures gives 11 cm^2, because the digit after the second significant figure is a 5 followed by non-zero digits, so we round the second figure up from 10 to 11. The choice 10.5 cm^2 keeps three significant figures, exceeding the precision justified by the data. The choice 10.54 cm^2 reports four figures and falsely implies very high precision. The choice 10 cm^2 rounds incorrectly, dropping the legitimate rounding-up of the leading figures. This procedure matches the NCERT rule for multiplication and division of measured quantities. A reasonableness check confirms it: the answer should carry no more reliability than the weakest measurement, which had only two significant figures.