Question

	measurement (using fractions)	measurement (in decimal form)	photo
book length (in):	10 (4/5)in	10.8 in
book width (in):	17/2 in	8.5in
area occupied by book (in²):

a) calculate the length of the long side of the book in micrometers. use dimensional analysis and show work below:
b) calculate the length of the shorter side of the book in kilometers. use dimensional analysis and show work below:
c) calculate the area occupied by the book (a = l x w) in square inches and input the area into the table above. use dimensional analysis to convert the area to acres, given 1 acre = 43,560 ft².

Explanation:

Part (a)

Step1: Identify the long side

The book length is \( 10.8 \) in and width is \( 8.5 \) in. So the long side is \( 10.8 \) in.

Step2: Convert inches to micrometers

We know that \( 1 \) inch \( = 2.54 \) centimeters, \( 1 \) centimeter \( = 10^4 \) micrometers. So the conversion factor from inches to micrometers is \( 2.54\times10^4 \) micrometers per inch.
Multiply the length in inches by the conversion factor: \( 10.8 \text{ in} \times 2.54\times 10^{4} \frac{\mu\text{m}}{\text{in}} \)

Step3: Calculate the result

\( 10.8\times2.54\times 10^{4}=10.8\times25400 = 274320 \) micrometers.

Step1: Identify the short side

The shorter side is the width, which is \( 8.5 \) in.

Step2: Convert inches to kilometers

We know that \( 1 \) inch \( = 2.54 \) centimeters, \( 1 \) meter \( = 100 \) centimeters, \( 1 \) kilometer \( = 1000 \) meters. So the conversion factor from inches to kilometers is \( \frac{2.54}{100\times1000\times100} \) kilometers per inch (since \( 1\ \text{km}=10^5\ \text{cm} \), so \( 1\ \text{in}=\frac{2.54}{10^5}\ \text{km} \)).
Multiply the width in inches by the conversion factor: \( 8.5 \text{ in} \times \frac{2.54}{10^{5}} \frac{\text{km}}{\text{in}} \)

Step3: Calculate the result

\( 8.5\times\frac{2.54}{10^{5}}=\frac{8.5\times2.54}{10^{5}}=\frac{21.59}{10^{5}} = 2.159\times 10^{-4} \) kilometers.

Step1: Calculate the area in square inches

The area \( A = l\times w \), where \( l = 10.8 \) in and \( w = 8.5 \) in. So \( A=10.8\times8.5 = 91.8\ \text{in}^2 \)

Step2: Convert square inches to square feet

We know that \( 1 \) foot \( = 12 \) inches, so \( 1\ \text{ft}^2=(12\ \text{in})^2 = 144\ \text{in}^2 \). The conversion factor from square inches to square feet is \( \frac{1}{144}\ \text{ft}^2/\text{in}^2 \)
So area in square feet: \( 91.8\ \text{in}^2\times\frac{1}{144}\ \frac{\text{ft}^2}{\text{in}^2}=\frac{91.8}{144}\approx0.6375\ \text{ft}^2 \)

Step3: Convert square feet to acres

Given \( 1 \) acre \( = 43560\ \text{ft}^2 \), the conversion factor is \( \frac{1}{43560}\ \text{acres/ft}^2 \)
So area in acres: \( 0.6375\ \text{ft}^2\times\frac{1}{43560}\ \frac{\text{acres}}{\text{ft}^2}=\frac{0.6375}{43560}\approx1.463\times 10^{-5}\ \text{acres} \)

Answer:

The length of the long side in micrometers is \( \boldsymbol{274320\ \mu\text{m}} \)

Part (b)