Question 14 (Essay Worth 12 points)
(Scientific Notation in the Real World HC)
A company is designing a rectangular computer chip that is $5.13 \times 10^{-7}$ meters long and $3.3 \times 10^{-9}$ meters wide.
Part A: Determine the area of the compufer chip. Show every step of your work. (3 points)
Part B: Write the area in scientific notation with the correct number of significant digits, and label with the appropriate units. (3 points)
Part c: Determine the perimeter of the computer chip. Show every step of your work. (3 points)
Part D: Write the perimeter in scientific notation with the correct number of significant digits, and label with the appropriate units (3 points)
Answer
For Part D, we write the perimeter in scientific notation with the correct number of significant digits. The length has more decimal places than the width, so our answer should have the same number of decimal places as the width. Therefore, the perimeter of the computer chip is \(\boxed{1.03 \times 10^{-6} \, \text{meters}}\).
Step 1 ：Given the length of the computer chip is \(5.13 \times 10^{-7}\) meters and the width is \(3.3 \times 10^{-9}\) meters.
Step 2 ：For Part A, we calculate the area of the computer chip. The area of a rectangle is given by the formula length * width. So, we multiply \(5.13 \times 10^{-7}\) meters and \(3.3 \times 10^{-9}\) meters to get the area.
Step 3 ：The calculated area is \(1.6929000000000002 \times 10^{-15}\) square meters.
Step 4 ：For Part B, we write the area in scientific notation with the correct number of significant digits. Both the length and width have two significant digits, so our answer should also have two significant digits. Therefore, the area of the computer chip is \(\boxed{1.69 \times 10^{-15} \, \text{meters}^2}\).
Step 5 ：For Part C, we calculate the perimeter of the computer chip. The perimeter of a rectangle is given by the formula 2*(length + width). So, we add \(5.13 \times 10^{-7}\) meters and \(3.3 \times 10^{-9}\) meters and then multiply the result by 2 to get the perimeter.
Step 6 ：The calculated perimeter is \(1.0326 \times 10^{-6}\) meters.
Step 7 ：For Part D, we write the perimeter in scientific notation with the correct number of significant digits. The length has more decimal places than the width, so our answer should have the same number of decimal places as the width. Therefore, the perimeter of the computer chip is \(\boxed{1.03 \times 10^{-6} \, \text{meters}}\).
