Your friend says that the product of 4.8 x 10^8 and 2 x 10^-3 is 5.6 x 10^-5. Is this answer correct? Explain.
Understand the Problem
The question is asking whether the product of 4.8 x 10^8 and 2 x 10^-3 equals 5.6 x 10^5 and to explain the correctness of this statement.
Answer
The answer is incorrect; the product is \(9.6 \times 10^5\).
Answer for screen readers
The correct product is (9.6 \times 10^5), so the statement is incorrect.
Steps to Solve
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Calculate the product of the coefficients We need to multiply the coefficients (4.8) and (2): [ 4.8 \times 2 = 9.6 ]
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Calculate the product of the powers of ten Now, we will multiply the powers of ten: [ 10^8 \times 10^{-3} = 10^{8 + (-3)} = 10^{5} ]
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Combine the results Now we can combine the results from steps 1 and 2: [ 9.6 \times 10^5 ]
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Compare with given statement Finally, compare the calculated product (9.6 \times 10^5) with your friend's statement (5.6 \times 10^5).
The correct product is (9.6 \times 10^5), so the statement is incorrect.
More Information
The product of two numbers in scientific notation is determined by multiplying the coefficients and adding the exponents of the ten powers.
Tips
- Miscalculating the multiplication of coefficients.
- Adding exponents incorrectly when multiplying powers of ten.
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