A company is designing a rectangular computer chip that is 5.13 × 10^−7 meters long and 3.3 × 10^−9 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 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)

[tex]\boxed{\begin{minipage}{3.5cm}\underline{Area of a rectangle}\\\\$A=w\:l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

Part A

Given:

w = 3.3 × 10⁻⁹
l = 5.13 × 10⁻⁷

Substitute the given values into the formula for area of a rectangle and solve for A:

[tex]\implies A=(3.3 \times 10^{-9}) \times (5.13 \times 10^{-7})[/tex]

[tex]\implies A=3.3 \times 10^{-9} \times 5.13 \times 10^{-7}[/tex]

[tex]\implies A=3.3 \times 5.13 \times 10^{-9}\times 10^{-7}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies A=16.929 \times 10^{(-9+(-7))}[/tex]

[tex]\implies A=16.929 \times 10^{(-9-7)}[/tex]

[tex]\implies A=16.929 \times 10^{-16}[/tex]

Part B

Scientific notation is written in the form of a × 10ⁿ where 1 ≤ a < 10 and n is any positive or negative whole number.

To write the area from Part A in scientific notation, move the decimal point of a back one place, which means the power of 10 (n) should be increased by 1.

[tex]\implies A=1.6929 \times 10^{-16+1}[/tex]

[tex]\implies A=(1.6929\times 10^{-15})\; \sf m^2[/tex]

Part C

[tex]\boxed{\begin{minipage}{3.8cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

Given:

w = 3.3 × 10⁻⁹
l = 5.13 × 10⁻⁷

Substitute the given values into the formula for perimeter of a rectangle and solve for P:

[tex]\implies P=2\left[(3.3 \times 10^{-9}) + (5.13 \times 10^{-7})\right][/tex]

[tex]\implies P=2(0.0000000033+0.000000513)[/tex]

[tex]\implies P=0.0000010326\; \sf m[/tex]

Part D

Scientific notation is written in the form of a × 10ⁿ where 1 ≤ a < 10 and n is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one digit to the left of the decimal point.

The number of times you have moved the decimal point is the power of 10 (the value of n).

If the decimal point has moved to the left, the power is positive.
If the decimal point has moved to the right, the power is negative.

To convert 0.0000010326 to scientific notation:

Move the decimal point 6 places to the right so that a = 1.0326.
As the decimal point has been moved 6 places the right, n = -6.

[tex]\implies P=(1.0326\times10^{-6})\; \sf m[/tex]