Multiply in Scientific Notation Practice

Question

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5 of 55 of 5 Items

Question
In a given year, about 1.52×1010
pieces of first-class mail are delivered in the U.S. If each piece of mail carries a stamp costing $0.55, what is the total cost in dollars to deliver all the pieces? Write the answer in scientific notation, expressed to the exact decimal place.

Answer 1

To find the total cost of delivering all the pieces of mail, you can multiply the number of pieces of mail by the cost of each stamp.

The number of pieces of mail is given as: \[ 1.52 \times 10^{10} \]

The cost of each stamp is: \[ 0.55 \]

Now, let's perform the multiplication:

1. Multiply the decimal numbers: \[ 1.52 \times 0.55 = 0.836 \]

2. Next, we combine the scientific notation: Since we're multiplying by \( 10^{10} \), we write it as follows: \[ 0.836 \times 10^{10} \]

3. Finally, to express \( 0.836 \) in scientific notation, we can write it as: \[ 8.36 \times 10^{-1} \]

Now combine it with \( 10^{10} \): \[ 8.36 \times 10^{-1} \times 10^{10} = 8.36 \times 10^{10 - 1} = 8.36 \times 10^{9} \]

Thus, the total cost in dollars to deliver all the pieces of first-class mail is: \[ \boxed{8.36 \times 10^9} \]