Question

A company is designing a rectangular computer chip that is 7.18 x 1077 meters long and 3.4 x 109 meters wide. Part A: Determine the area of the computer 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 po 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.​

Answer 1

The area of the computer chip is 2.4 x 10^87 square meters, with the area expressed in scientific notation with appropriate significant digits. The perimeter is approximately 1.4 x 10^78 meters, simplified to the correct number of significant figures.

Step-by-step explanation:

To calculate the area of a rectangular computer chip, we multiply the length by the width. Given the dimensions are 7.18 x 1077 meters and 3.4 x 109 meters, the area is:

Area = length × width = (7.18 x 1077) × (3.4 x 109)

Using the rules of multiplication for scientific notation:

Area = 7.18 × 3.4 x 1077 + 9

= 24.412 x 1086 square meters

After adjusting significant figures to match the least precise measurement of 3.4 (2 significant digits), the area is:

Area = 2.4 x 1087 square meters

For part C, to get the perimeter of the rectangle, we add twice the length and twice the width:

Perimeter = 2 × length + 2 × width

= 2(7.18 x 1077) + 2(3.4 x 109)

Converting the numerals into a compatible form to add them yields:

Perimeter = 1.436 x 1078 meters (adding length) + 6.8 x 1010 meters (adding width) and since the first term dominates:

Perimeter = 1.4 x 1078 meters (correct to 2 significant digits)