Significant Figures And Errors

NCERT Class 11, Chapter 2 lays down the rule that in multiplication or division, the result must be rounded to the same number of significant figures as the measured quantity carrying the fewest significant figures. The length 12.34 cm has four significant figures, while the width 5.6 cm has only two significant figures. The product $12.34\times 5.6=69.104{\text{ cm}}^2$, but because the least precise factor limits the result, the area must be reported with only two significant figures, giving $69{\text{ cm}}^2$. The option of four significant figures is wrong because it follows the more precise length rather than the limiting width. The option of three significant figures is wrong because no measured quantity here has three, so this splits the difference incorrectly. The option of six significant figures is wrong because it retains all the digits from raw multiplication, falsely implying precision the data cannot support. It is important to distinguish this from the rule for addition and subtraction, where it is the number of decimal places, not significant figures, that governs the result; mixing the two rules is a common error. Rounding to significant figures is not merely a stylistic choice but a faithful statement of how well the quantity is actually known. A consistency check confirms that a result can never be more precise than its least precise input, so two significant figures, giving 69 square centimetres, is the honest report.