Question

exercise 2 with a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. with a micrometer calipers, you measure the width of the rectangle to be 5.98 mm. use a correct number of significant figures : given : length (l) = 12 mm width (w) = 5.98 mm

Explanation:

Step1: Recall significant - figure rules for multiplication

When multiplying two measured values, the result should have the same number of significant figures as the value with the fewest significant figures.
The length $l = 12\ mm$ has 2 significant figures, and the width $w=5.98\ mm$ has 3 significant figures.

Step2: Calculate the area of the rectangle

The area of a rectangle is given by $A = l\times w$. Substitute $l = 12\ mm$ and $w = 5.98\ mm$ into the formula: $A=12\times5.98 = 71.76\ mm^{2}$.

Step3: Round the result to the correct number of significant figures

Since the length has 2 significant figures, we round the area to 2 significant figures. Rounding 71.76 to 2 significant figures gives 72 $mm^{2}$.

Answer:

$72\ mm^{2}$