The size of a dollar bill is 6.6 cm wide, 15.6 cm long and 0.109 mm in thickness. Approximately how many dollar bills are in a 0.24-inch stack? The # dollar bills, N=
The correct answer and explanation is :
To determine how many dollar bills are in a 0.24-inch stack, we need to consider the thickness of a single dollar bill and then calculate how many such thicknesses fit into the given stack height. Here’s how we approach it:
Step 1: Convert inches to millimeters
First, we need to convert the height of the stack (0.24 inches) into millimeters since the thickness of the dollar bill is provided in millimeters.
1 inch = 25.4 millimeters
So:
[
0.24 \text{ inches} \times 25.4 \text{ mm/inch} = 6.096 \text{ mm}
]
Thus, the stack height is 6.096 mm.
Step 2: Find the thickness of a single dollar bill
The thickness of a dollar bill is given as 0.109 mm.
Step 3: Calculate the number of dollar bills in the stack
Now, we can find how many dollar bills fit into a stack of 6.096 mm by dividing the total height of the stack by the thickness of a single dollar bill.
[
N = \frac{6.096 \text{ mm}}{0.109 \text{ mm/bill}} \approx 55.9
]
Since the number of dollar bills must be a whole number, we round this result to the nearest whole number:
[
N \approx 56
]
Conclusion:
There are approximately 56 dollar bills in a 0.24-inch stack.
Explanation:
The calculation follows a straightforward method of converting units and dividing the stack height by the thickness of a single bill. Understanding that the thickness of a dollar bill is relatively small compared to the overall height of the stack allows us to estimate the number of bills. The conversion from inches to millimeters ensures consistency in the units, and rounding the result gives us the closest integer number of bills that would fit in the stack.