Indeed, this thought experiment illustrates how vast such a hypothetical stack would be. Let's break down the calculation and verify the result for insight:

1. Thickness of a Single Bill: Each $100 bill is approximately 0.0043 inches thick.
2. Total Number of Bills: We have $2.4999999999999997 \times 10^{31}$ bills.

To find the total height of the stack:

• First, multiply the thickness of each bill by the number of bills:

  $\text{Total height in inches} = 0.0043 \times 2.4999999999999997 \times 10^{31} \approx 1.075 \times 10^{29} \text{ inches}$

3. Converting to Light-Years:

   • There are $63,360$ inches in a mile.
   • There are $5.879 \times 10^{12}$ miles in a light-year.

   Therefore:

   $\text{Total height in light-years} = \frac{1.075 \times 10^{29}}{63,360 \times 5.879 \times 10^{12}} \approx 2.87 \times 10^{13} \text{ light-years}$

Conclusion

The height of this theoretical stack would indeed be about $2.87 \times 10^{13}$ light-years, vastly outscaling the observable universe's diameter of 93 billion (or $9.3 \times 10^{10}$) light-years. This result showcases how enormous numbers can quickly scale into cosmic proportions, highlighting the sheer vastness of exponential growth.

Would you like more details or have any questions?

Related Questions

1. What would the weight of such a stack of bills be?
2. How many $100 bills would it take to reach the height of Mount Everest?
3. How much money (in dollars) would this stack of bills represent?
4. How would the size of this stack compare to the Milky Way galaxy's diameter?
5. If you added one bill per second, how long would it take to complete this stack?

Tip

When working with extreme values, converting units step-by-step helps ensure precision and clarity in the results.