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

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A penny is

6 \times 10^{-2}

inches thick. The Empire State Building has a height of

1,250

feet, or

1.5 \times 10^{4}

inches. How many pennies would you have to stack to reach the top of the Empire State Building?

\newline

Write your answer in scientific notation.

\newline

______ pennies

\newline

Penny Thickness: Penny thickness = $6 \times 10^{-2}$ inches. $\newline$ Empire State Building height = $1.5 \times 10^{4}$ inches. $\newline$ To find the number of pennies, divide the height of the building by the thickness of a penny.
Empire State Building Height: Number of pennies = $(1.5 \times 10^4 \text{ inches}) / (6 \times 10^{-2} \text{ inches})$ . Simplify the division by canceling out the inches and dividing the numbers.
Calculate Number of Pennies: Number of pennies = $(1.5 / 6) \times (10^4 / 10^{-2})$ . Calculate the division and subtract the exponents.
Simplify Division: Number of pennies = $0.25 \times 10^{4 - (-2)}$ . $\newline$ Simplify the exponent by adding.
Combine Exponents: Number of pennies = $0.25 \times 10^6$ . Convert $0.25$ to scientific notation to combine with the exponent.
Convert to Scientific Notation: $0.25$ is the same as $2.5 \times 10^{-1}$ , so we have: $\newline$ Number of pennies = $(2.5 \times 10^{-1}) \times 10^6$ . $\newline$ Multiply the coefficients and add the exponents.
Multiply Coefficients: Number of pennies = $2.5 \times 10^{6 - 1}$ . Simplify the exponent by subtracting.
Simplify Exponent: Number of pennies = $2.5 \times 10^5$ . This is the final answer in scientific notation.

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