Answer :
Sure! Let's solve this step-by-step:
### Part (a): How thick is each piece of paper?
1. Total Thickness of Stack: We know that a stack of 500 sheets of paper is 2.25 inches thick.
2. Number of Sheets: There are 500 sheets in the stack.
3. Find Thickness per Sheet: To find the thickness of just one sheet of paper, divide the total thickness by the number of sheets.
[tex]\[
\text{Thickness per sheet} = \frac{2.25 \text{ inches}}{500 \text{ sheets}}
\][/tex]
4. Compute the Result: The thickness of each sheet is 0.0045 inches.
### Part (b): Checking the Result using Multiplication
To verify our calculation, we will use multiplication:
1. Multiply the Thickness per Sheet by the Total Number of Sheets:
[tex]\[
0.0045 \text{ inches/sheet} \times 500 \text{ sheets} = 2.25 \text{ inches}
\][/tex]
2. Check if the Result Matches: The result should equal the original thickness of the stack, confirming that our calculation is correct. In this case, we indeed get 2.25 inches, so our calculation is verified and accurate.
This step-by-step solution demonstrates that each sheet of paper is 0.0045 inches thick, as calculated, and it matches the given stack thickness when multiplied by the number of sheets.
### Part (a): How thick is each piece of paper?
1. Total Thickness of Stack: We know that a stack of 500 sheets of paper is 2.25 inches thick.
2. Number of Sheets: There are 500 sheets in the stack.
3. Find Thickness per Sheet: To find the thickness of just one sheet of paper, divide the total thickness by the number of sheets.
[tex]\[
\text{Thickness per sheet} = \frac{2.25 \text{ inches}}{500 \text{ sheets}}
\][/tex]
4. Compute the Result: The thickness of each sheet is 0.0045 inches.
### Part (b): Checking the Result using Multiplication
To verify our calculation, we will use multiplication:
1. Multiply the Thickness per Sheet by the Total Number of Sheets:
[tex]\[
0.0045 \text{ inches/sheet} \times 500 \text{ sheets} = 2.25 \text{ inches}
\][/tex]
2. Check if the Result Matches: The result should equal the original thickness of the stack, confirming that our calculation is correct. In this case, we indeed get 2.25 inches, so our calculation is verified and accurate.
This step-by-step solution demonstrates that each sheet of paper is 0.0045 inches thick, as calculated, and it matches the given stack thickness when multiplied by the number of sheets.
