Question

question 2 (1 point)
the length and width of a rectangle are 1.125 m and 0.606 m, respectively. you calculate the rectangles perimeter by adding these and multiplying by two. your calculators display reads 3.462. to the correct number of significant figures, this should be written as
3.5 m.
3.46 m.
3.462 m.
3.4620 m.

Explanation:

Step1: Determine the number of decimal places in the given values

The length \(1.125\) m has three decimal places and the width \(0.606\) m has three decimal places.

Step2: Calculate the sum of length and width

\(1.125 + 0.606=1.731\)

Step3: Multiply the sum by 2

\(2\times1.731 = 3.462\)

Step4: Consider significant - figure rules for addition and multiplication

When adding \(1.125\) and \(0.606\) (both have three decimal places), the sum \(1.731\) has three decimal places. When multiplying \(1.731\) (four significant figures) by \(2\) (an exact number), the result should have the same number of significant figures as the non - exact number. Here, \(1.731\) has four significant figures. But looking at the original values \(1.125\) (four significant figures) and \(0.606\) (three significant figures), when we add \(1.125+0.606 = 1.731\) (the rule for addition: the result should have the same number of decimal places as the number with the least number of decimal places among the addends. Here both have three decimal places). Then when we multiply by \(2\) (an exact number), the number of significant figures is determined by the sum \(1.731\). However, if we consider the original values \(1.125\) (four significant figures) and \(0.606\) (three significant figures), the least number of significant figures in the original data for the perimeter calculation (which is based on addition and then multiplication) - the addition \(1.125 + 0.606\) is precise to the thousandth place. But when we look at the significant - figure rules for the final result: the original numbers \(1.125\) (four significant figures) and \(0.606\) (three significant figures). The rule for multiplication/division after addition/subtraction: first do the addition \(1.125+0.606 = 1.731\) (three decimal places, four significant figures). Then \(2\times1.731\). Since \(2\) is exact, the result \(3.462\) should be rounded to three significant figures (because \(0.606\) has three significant figures). Rounding \(3.462\) to three significant figures gives \(3.46\).

Answer:

\(3.46\space m\)