A company is designing a rectangular computer chip that is 8.14 × 10−7 meters long and 3.6 × 10−9 meters wide.
Part A: Determine the area of the computer chip. Show every step of your work.
Part B: Write the area in scientific notation with the correct number of significant digits, and label with the appropriate units.
Part C: Determine the perimeter of the computer chip. Show every step of your work.
Part D: Write the perimeter in scientific notation with the correct number of significant digits, and label with the appropriate units.
Part A:
To find the area of the computer chip, we use the formula: Area = length × width.
Given:
Length = 8.14 × 10^(-7) meters
Width = 3.6 × 10^(-9) meters
Area = (8.14 × 10^(-7)) × (3.6 × 10^(-9))
= 2.9304 × 10^(-15) square meters
Part B:
The area is in scientific notation with the correct number of significant digits when it is expressed as a single non-zero digit (the first digit) multiplied by a power of 10. In this case, the first digit is 2.9304 and the power of 10 is -15.
Area = 2.9304 × 10^(-15) square meters
Part C:
To find the perimeter of the computer chip, we use the formula: Perimeter = 2(length + width).
Given:
Length = 8.14 × 10^(-7) meters
Width = 3.6 × 10^(-9) meters
Perimeter = 2((8.14 × 10^(-7)) + (3.6 × 10^(-9)))
= 2(8.14 × 10^(-7) + 3.6 × 10^(-9))
= 2(8.14 × 10^(-7)) + 2(3.6 × 10^(-9))
= 1.628 × 10^(-6) + 7.2 × 10^(-9)
= 1.628 × 10^(-6) meters
Part D:
The perimeter is in scientific notation with the correct number of significant digits when it is expressed as a single non-zero digit (the first digit) multiplied by a power of 10. In this case, the first digit is 1.628 and the power of 10 is -6.
Perimeter = 1.628 × 10^(-6) meters
Part A: To determine the area of the computer chip, we need to multiply its length and width.
Area = length × width
Area = (8.14 × 10^-7 m) × (3.6 × 10^-9 m)
Now we multiply the numbers outside the power of 10:
Area = (8.14 × 3.6) × (10^-7 × 10^-9) m^2
Area = 29.304 × 10^-16 m^2
Part B: To write the area in scientific notation with the correct number of significant digits, we round the result to the appropriate number of significant figures. Since both numbers given have 3 significant figures, we round our final answer to 3 significant figures as well.
Area = 2.93 × 10^-15 m^2
Part C: To determine the perimeter of the computer chip, we need to add up the lengths of all four sides.
Perimeter = 2(length + width)
Perimeter = 2(8.14 × 10^-7 m + 3.6 × 10^-9 m)
Perimeter = 2(8.14 × 10^-7 m) + 2(3.6 × 10^-9 m)
Perimeter = 16.28 × 10^-7 m + 7.2 × 10^-9 m
Part D: To write the perimeter in scientific notation with the correct number of significant digits, we round the result to the appropriate number of significant figures. Since both numbers given have 3 significant figures, we round our final answer to 3 significant figures as well.
Perimeter = 1.63 × 10^-6 m