Let's analyze this statement step-by-step and verify the claim. We are given:

• Thickness of a $100 bill: $0.0043$ inches
• Number of $100 bills in the stack: $2.4999999999999997 \times 10^{31}$
• Total height in inches: This is calculated as the product of the thickness per bill and the number of bills.

We want to verify whether this stack indeed extends beyond the observable universe, which has a diameter of 93 billion light-years.

Step 1: Calculate the Total Height in Inches

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

Step 2: Convert Inches to Light-Years

1 light-year = $5.8786254 \times 10^{12}$ miles
1 mile = $63,360$ inches
Therefore, 1 light-year in inches is: $1 \text{ light-year} = 5.8786254 \times 10^{12} \times 63,360 \approx 3.7245 \times 10^{17} \text{ inches}$

Now, we divide the total height by the number of inches in a light-year to find the height in light-years: $\text{Height in light-years} = \frac{1.075 \times 10^{29}}{3.7245 \times 10^{17}} \approx 2.887 \times 10^{11} \text{ light-years}$

Step 3: Compare to the Diameter of the Observable Universe

The diameter of the observable universe is approximately 93 billion light-years ($9.3 \times 10^{10}$ light-years). Comparing: $2.887 \times 10^{11} \text{ light-years} \gg 9.3 \times 10^{10} \text{ light-years}$

Conclusion

Indeed, the stack of these $100 bills would extend much further than the observable universe's diameter. The calculation shows that it would reach approximately 2.87 × 10^11 light-years, which is more than 3 times the diameter of the observable universe.

Would you like more details on any of the calculations or concepts involved?

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