Your breakdown is correct, and it clarifies where the error in the initial calculation likely occurred. Let's confirm the calculations step-by-step:

Step 1: Calculate the Total Height of the Stack in Inches

Given:

• Thickness of one bill, $T = 0.0043$ inches.
• Total number of bills, $N = 2.4999999999999997 \times 10^{31}$.

The height $H$ of the stack in inches is: $H = N \times T = 2.4999999999999997 \times 10^{31} \times 0.0043$ $H \approx 1.075 \times 10^{29} \text{ inches}$

Step 2: Convert Inches to Miles

To convert inches to miles, use:

• 1 mile = 63,360 inches.

$H_{\text{miles}} = \frac{1.075 \times 10^{29}}{63,360}$ $H_{\text{miles}} \approx 1.697 \times 10^{24} \text{ miles}$

Step 3: Convert Miles to Light-Years

Using:

• 1 light-year ≈ $5.8786 \times 10^{12}$ miles.

$H_{\text{light-years}} = \frac{1.697 \times 10^{24}}{5.8786 \times 10^{12}}$ $H_{\text{light-years}} \approx 2.887 \times 10^{11} \text{ light-years}$

Conclusion

The correct height is approximately $2.887 \times 10^{11}$ light-years, which, while extremely large, does not exceed the observable universe's estimated diameter of about 93 billion light-years. Therefore, the height is indeed smaller than initially stated but remains extraordinarily large.

Would you like to go over any particular step in more detail?

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Related Questions:

1. How does the height of this stack compare to the Milky Way galaxy's diameter?
2. What would happen to the stack's height if the thickness of the bill increased to 0.005 inches?
3. How would we calculate this distance in terms of astronomical units (AU)?
4. How many times would this stack reach from Earth to the Andromeda Galaxy?
5. How does the speed of light relate to the calculated light-years in practical terms?

Tip: When converting between large units, always keep track of conversion factors precisely to avoid errors over magnitudes.