Significant Figures In Multiplication

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A surveyor multiplies a measured length of 4.2 m by a measured width of 3.15 m to find the area of a rectangular plot. How many significant figures should the reported area contain?

RankGuru · Accepted Answer

NCERT Class 11, Chapter 2 (Units and Measurements) states that in multiplication or division the result should retain only as many significant figures as the factor having the fewest significant figures. The length 4.2 m has two significant figures, while the width 3.15 m has three. The smaller count, two, controls the result. The raw product is 4.2 × 3.15 = 13.23 m^2, which must be rounded to two significant figures, giving 13 m^2. The option 3 is wrong because it borrows precision from the more precise width measurement. The option 4 is wrong as no factor has four significant figures to justify it. The option 1 is wrong since both measurements clearly contain more than a single reliable digit. A sanity check confirms that rounding 13.23 to two significant figures yields 13, which sensibly reflects the precision limit set by the coarser length measurement.

Significant Figures In Multiplication

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