To perform the operation of multiplying two numbers in scientific notation, you can follow these steps:
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Multiply the coefficients: Take the numerical parts (the coefficients) of both numbers and multiply them together.
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Add the exponents: Take the exponents of the base (which is usually 10) and add them together.
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Write in scientific notation: Format your result back into scientific notation, ensuring that the coefficient is between 1 and 10.
As an example, let's multiply \( (3.2 \times 10^4) \) and \( (2.5 \times 10^3) \):
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Multiply the coefficients: \[ 3.2 \times 2.5 = 8.0 \]
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Add the exponents: \[ 4 + 3 = 7 \]
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Combine: \[ 8.0 \times 10^7 \]
Since the coefficient \( 8.0 \) is not between 1 and 10, we adjust it to: \[ 8.0 = 8.0 \times 10^0 \] Combining this with \( 10^7 \): \[ 8.0 \times 10^7 = 0.8 \times 10^8 \quad (\text{now the coefficient is between 1 and 10}) \]
So, the final result in scientific notation is: \[ 0.8 \times 10^8 \]
Thus, the multiplication of \( (3.2 \times 10^4) \) and \( (2.5 \times 10^3) \) results in \( 0.8 \times 10^8 \).
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