Question

question 18 (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 significant figures in given values

The length \(1.125\) m has \(4\) significant figures. The width \(0.606\) m has \(3\) significant figures. When adding or subtracting, the result should be rounded to the least number of decimal places. When multiplying or dividing, the result should be rounded to the least number of significant figures. Here, we first add \(1.125 + 0.606=1.731\) (addition, decimal - place rule: \(1.125\) has three decimal places, \(0.606\) has three decimal places), then multiply by \(2\) (multiplication, significant - figure rule). The sum \(1.731\) (from addition) is then multiplied by \(2\). The number \(1.731\) has \(4\) significant figures and \(2\) is an exact number (in the formula \(P = 2(l + w)\), the \(2\) is a defined multiplier, not a measured value). But we can also consider the original measured values. The width \(0.606\) has \(3\) significant figures.

Step2: Round the final result

The calculator result is \(3.462\). Since the least number of significant figures in the original measured values (considering the rules for perimeter formula \(P=2(l + w)\) and significant - figure rules for mixed operations, focusing on the measured values \(l = 1.125\) and \(w=0.606\), where \(w\) has \(3\) significant figures) the result should be rounded to \(3\) significant figures. \(3.462\approx3.46\)

Answer:

3.46 m.