Math Problem Statement

Your calculation seems to contain a significant error in the height of the stack of bills. Let's break it down:

  1. Thickness of a single bill: Approximately 0.0043 inches.
  2. Number of bills: (2.4999999999999997 \times 10^{31}).

To find the total height of the stack, you would multiply the number of bills by the thickness:

[ \text{Total height} = 2.4999999999999997 \times 10^{31} , \text{bills} \times 0.0043 , \text{inches} ]

Calculating this gives:

[ \text{Total height} \approx 1.074 \times 10^{29} , \text{inches} ]

To convert inches to light-years:

  1. There are 63,360 inches in a mile and about 5.8786 × 10^12 miles in a light-year.

So, the conversion from inches to light-years would be:

[ \text{Total height in light-years} \approx \frac{1.074 \times 10^{29} , \text{inches}}{63,360 , \text{inches/mile} \times 5.8786 \times 10^{12} , \text{miles/light-year}} ]

Calculating that gives approximately (2.0 \times 10^{22}) light-years, which is much smaller than the observable universe's diameter of about 93 billion light-years.

So, the claim that it would stretch for (2.87 \times 10^{13}) light-years is incorrect; it's still an enormous number, but it doesn't surpass the size of the observable universe.

Solution

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Unit Conversion
Scientific Notation

Formulas

Total height = Number of bills × Thickness of a single bill
Inches to miles: miles = inches / 63,360
Miles to light-years: light-years = miles / 5.8786 × 10^12

Theorems

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Suitable Grade Level

Grades 11-12