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A penny is 6×10−26 \times 10^{-2} inches thick. The Empire State Building has a height of 1,2501,250 feet, or 1.5×1041.5 \times 10^{4} inches. How many pennies would you have to stack to reach the top of the Empire State Building?\newlineWrite your answer in scientific notation.\newline______ pennies\newline

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Q. A penny is 6×10−26 \times 10^{-2} inches thick. The Empire State Building has a height of 1,2501,250 feet, or 1.5×1041.5 \times 10^{4} inches. How many pennies would you have to stack to reach the top of the Empire State Building?\newlineWrite your answer in scientific notation.\newline______ pennies\newline
  1. Penny Thickness: Penny thickness = 6×10−26 \times 10^{-2} inches.\newlineEmpire State Building height = 1.5×1041.5 \times 10^{4} inches.\newlineTo find the number of pennies, divide the height of the building by the thickness of a penny.
  2. Empire State Building Height: Number of pennies = (1.5×104 inches)/(6×10−2 inches)(1.5 \times 10^4 \text{ inches}) / (6 \times 10^{-2} \text{ inches}). Simplify the division by canceling out the inches and dividing the numbers.
  3. Calculate Number of Pennies: Number of pennies = (1.5/6)×(104/10−2)(1.5 / 6) \times (10^4 / 10^{-2}). Calculate the division and subtract the exponents.
  4. Simplify Division: Number of pennies = 0.25×104−(−2)0.25 \times 10^{4 - (-2)}.\newlineSimplify the exponent by adding.
  5. Combine Exponents: Number of pennies = 0.25×1060.25 \times 10^6. Convert 0.250.25 to scientific notation to combine with the exponent.
  6. Convert to Scientific Notation: 0.250.25 is the same as 2.5×10−12.5 \times 10^{-1}, so we have:\newlineNumber of pennies = (2.5×10−1)×106(2.5 \times 10^{-1}) \times 10^6.\newlineMultiply the coefficients and add the exponents.
  7. Multiply Coefficients: Number of pennies = 2.5×106−12.5 \times 10^{6 - 1}. Simplify the exponent by subtracting.
  8. Simplify Exponent: Number of pennies = 2.5×1052.5 \times 10^5. This is the final answer in scientific notation.

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