Questions: The density of aluminum is 2.70 g/cm^3. A square piece of aluminum foil 22.86 cm on one side weighs 2.568 g. What is the thickness of the foil in mm? Express your answer in scientific notation with 3 significant figures. Do not include the units The accepted format for scientific notation answers in Canvas is m^* 10^ n, where m represents the coefficient (the number being multiplied), the asterisk represents the multiplication function, and ^ n represents the exponent. Example: 245^* 10^ 2, 4.55^* 10^ -3

Solution Steps

The volume \( V \) of the aluminum foil can be calculated using the formula for density:

\[ V = \frac{\text{mass}}{\text{density}} \]

Given:

• Mass of the foil = \( 2.568 \, \text{g} \)
• Density of aluminum = \( 2.70 \, \text{g/cm}^3 \)

Substitute the values:

\[ V = \frac{2.568}{2.70} = 0.9511 \, \text{cm}^3 \]

The area \( A \) of the square piece of aluminum foil is given by:

\[ A = \text{side}^2 \]

Given:

• Side of the square = \( 22.86 \, \text{cm} \)

Substitute the value:

\[ A = 22.86^2 = 522.2916 \, \text{cm}^2 \]

The thickness \( t \) of the foil can be calculated using the formula:

\[ t = \frac{V}{A} \]

Substitute the values:

\[ t = \frac{0.9511}{522.2916} = 0.001821 \, \text{cm} \]

Convert the thickness from cm to mm (1 cm = 10 mm):

\[ t = 0.001821 \times 10 = 0.01821 \, \text{mm} \]

Express the thickness in scientific notation with 3 significant figures:

\[ t = 1.82^{*} 10^{\wedge} -2 \]

Final Answer