Find 7.2 x 10^-8 × 3 x 10^-2. Write your answer in scientific notation.
Understand the Problem
The question is asking us to find the product of two scientific notation values: 7.2 × 10^−8 and 3 × 10^−2. We need to perform the multiplication and express the answer in scientific notation.
Answer
The product is $2.16 \times 10^{-9}$.
Answer for screen readers
The final answer in scientific notation is: $$ 2.16 \times 10^{-9} $$
Steps to Solve
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Multiply the coefficients To find the product of the two scientific notation values, we first multiply the coefficients: $$ 7.2 \times 3 = 21.6 $$
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Add the exponents Next, we add the exponents from the powers of ten. The original powers are $10^{-8}$ and $10^{-2}$, so we have: $$ -8 + (-2) = -10 $$
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Combine the results Now we can combine the results of the multiplication and the exponent addition into scientific notation: $$ 21.6 \times 10^{-10} $$
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Adjust to standard scientific notation In standard scientific notation, the coefficient must be between 1 and 10. Therefore, we rewrite $21.6$ as: $$ 2.16 \times 10^1 $$ So, we have: $$ 2.16 \times 10^1 \times 10^{-10} $$
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Final exponent adjustment Now, combine the exponents: $$ 2.16 \times 10^{1 - 10} = 2.16 \times 10^{-9} $$
The final answer in scientific notation is: $$ 2.16 \times 10^{-9} $$
More Information
When multiplying numbers in scientific notation, it's important to individually multiply the coefficients and add the exponents. The result must be adjusted to ensure the coefficient is between 1 and 10.
Tips
- Incorrectly adjusting the coefficient: Not ensuring that the coefficient stays between 1 and 10 is a common mistake. Always convert it as needed.
- Forgetting to add exponents: Remember to add the exponents of the powers of ten correctly.
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