Question

question 6 (1 point) ✓ saved
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: Recall the rule for significant figures in addition

When adding or subtracting, the result should be rounded to the least number of decimal places among the values being added or subtracted. Here, \(1.125 + 0.606=1.731\) (no rounding needed at this addition - subtraction step as we are following the perimeter formula \(P = 2(l + w)\) where \(l = 1.125\) (three decimal places) and \(w=0.606\) (three decimal places)). Then \(P=2\times1.731 = 3.462\).

Step2: Check the significant - figure rules for multiplication

When multiplying, the number of significant figures in the result is determined by the number with the fewest significant figures in the multiplication. \(2\) is an exact number (in the formula \(P = 2(l + w)\), the \(2\) comes from the definition of perimeter of a rectangle, so it has infinite significant figures). The sum \(l + w=1.731\) has four significant figures. So \(3.462\) (from \(2\times1.731\)) should be written as \(3.462\) (since \(2\) is exact and \(1.731\) has four significant figures).

Answer:

\(3.462\space m\)